As long as it's within the same Generation you can trade Eggs. The only time you can't trade Eggs is when you're transferring them to the next Generation (so you can't transfer an Egg in your Sapphire version to your Diamond version, you have to hatch them and then use Pal Park to transfer them where you catch them). The only reason I didn't trade Eggs is because I needed the Pokemon I was sending over to hold items which Eggs can't do.
ANYWAY, Pokemon White 2 story time:
So last time I stopped before I ventured through Route 13 (which I accidentally called Route 14 in observation #11 in my last post). Not only because I finished the Forgotten Item quest, but also because I wanted to train a bit. So after flying back to Mistralton City and grinded on the Breeder on Route 7 (hey, if I'm going to train I might as well make some money off it, plus trainer Pokemon do give out more experience) among other things (like Surfing to locations I could now), I flew back to Undella and now ready to see what Route 13 has in store for me:
1. And one of these things is a Legendary battle! You remember when I encountered Cobalion and after Sage Rood told me to go catch it I joked that by now it's probably on the other side of Unova... as it turns out I was right! Just outside of Lacunosa Town there was Cobalion, sitting and waiting for me. When I approached it looked at my direction though like most Legendaries it waited for me to interact with it before starting the battle. After saving I engaged the battle and now Cobalion is sitting pretty in my PC at Level 45 (meaning it knows Sacred Sword, Iron Head, Retaliate, and Helping Hand).
2. Entering Lacunosa Town victoriously, Professor Juniper and Bianca stopped me and Professor Juniper tells me she has a story she wants me to hear (Bianca also teased that she got here first using Fly, though considering in order to use Fly you needed to be at a location before and on my way here I caught a Legendary Pokemon, I think I actually won). So Juniper takes me to an old woman who tells us the story of the town, it had high walls built because a monster which came from a meteorite that fell was going out at night to eat people and Pokemon. Professor Juniper theorizes that since Reshiram and Zekrom we transformed into stones after their ancient battle then that could mean Kyurem also was. Apparently everyone does know about Kyurem and Bianca even suggests it doesn't come out during the day because it hates sunlight though Professor Juniper says they can't really say that for certain. Anyway Professor Juniper tells us to go to Opelucid City and here what Drayden has to say about Kyurem.
Though we aren't done in Lacunosa Town yet as Hugh is waiting for you at the town's exit into Route 12 on the lookout for Team Plasma. Of course, Zinzolin and a grunt appears and you do a double battle with Hugh and defeat them (BTW, for a guy who complains about the cold, Zinzolin uses ICE-type Pokemon). They run off with Hugh right on their tails and you too (sorta) as we enter into Route 12.
3. Entering Village Bridge (yeah, there was nothing on Route 12 except trainer, items, and wild Pokemon), it seems to have changed a bit as the Village Bridge Restaurant and been replaced by a tennis court (and on the other side is a basketball court), though you an find the chef now operating out of one of the houses however he doesn't do the waiter mini-game. Only other interesting spot is a new room open under the bridge where you find a girl practicing to sing but upon realizing you're there she pushes you out. I can't find any information on any events which occur with her so maybe something in the future?
4. Route 11 only has one thing to note aside from the usual, though this would normally be considered part of the usual: There's a Breeder here. She has 2 Pokemon at level 41 so their good to find off of if you need to before battling Drayden or Marlon.
5. Finally we get to Opelucid City and upon entering you'll meet Iris who asks if we're here to battle her "grandpa" Drayden though tells us they aren't related. She says Drayden is in the Gym though you can also go to Route 9 to train a bit and then leaves. BTW, Route 10 no longer exists in Black 2 & White 2, a landside happened on Victory Road and destroyed it and Route 10. Now while I can go battle Drayden now, let's go over and see how Route 9 is doing.
6. Nothing much is happening on Route 9. Went into Shopping Mall Nine which has an interesting "quest" where a girl gives you 1,200 Pokedollars to buy a Hyper Potion (she can't because she doesn't have any badges) though being I have a few free ones I found I gave her one of those so she rewards me with an Energy Root. Another interesting addition is that there's a maid who sells a certain item on a 10% discount, though when I talked to her the item was only a potion which, even with the discount, the ton of Fresh Water I have (and can buy from a Vending Machine upstairs) is still better. Hopefully she'll eventually discount vitamins. Tried crossing Tubeline Bridge however a guy stopped me from entering saying they were testing how many people could be on the bridge and they reached the limit (so if you reached the limit why are you still testing?).
7. Gym time. Depending on what version you have the Gym sort of changes, at least in appearance... actually only in color. The Gym puzzle has you "riding" on a dragon statue up against another dragon statue. If you're playing White 2 your dragon is white and the Gym's is black while in Black 2 it's the opposite. The puzzle involves your riding your dragon statue having it rise to that it's head is facing the head of the other Dragon (and, of course, Drayden is on the other Dragon's head), but in order to do so you need to battle at least one of the trainers on each "level" to be allowed to ride to the next. First there's the only one on the tail, however as you rise feet level you can battle one (or both) of two trainers: one which focuses on Defense and another who focuses on Offense (WARNING on the one with Defense, her Druddigon not only has the Rough Skin Ability but also has a Rocky Helmet. In other words, use Special Attacks for it). Arms (or front feet) level, one trainer does Rotation Battles while another does Triple Battles. Finally you get to Drayden at head level. It sort of reminds me of Petalburg Gym. Oh, and Drayden wasn't hard to beat, Flygon actually turned out to be useless as it was slower then most of Drayden's (and the otherGym Trainer's) Pokemon, however Emboar and his Hammer Arm picked up the slack. After getting the Badge, Drayden tells you to meet him in his house where they'll talk.
8. In Drayden's house, he explains how Reshiram and Zekrom were one Pokemon, but there's a third dragon made from what was left over: Kyurem. He wonders if there are any more dragons but tells you he's giving you an item that has been passed down from generations in his family since it's made from a same material found in Giant Chasm and Dragonspiral Tower: the DNA Splicers. Drayden says he doesn't know what the items did (yet you called them the DNA Splicers, a name which indicates its function...) however he knew he had to keep them safe until they were needed so he hid them where no one could get them.
Suddenly you hear an odd roar outside and when you do you'll see Team Plasma's Frigate FLYING over the city! Before you could think anything else, it then starts bombarding the city with a cannon which creates giant ice pillars all over the city. Zinzolin and a few grunts walk up to you and asks for the DNA Splicers, though it's mostly an empty threat since Zinzolin reveals that they can't fire any more shots (Hint if you want to become a villain: NEVER reveal the limitation of your devices. Zinzolin should have just said if they don't give the DNA Splicers they would fire more onto the city of Dragon-types. Then if they wanted to they could have a grunt become confused by this and accidentally reveal they can't fire again). Team Plasma starts running around the city to look for the DNA Splicers and Drayden says he needs our help to drive them out of Opelucid City. I actually ran around the city (by the way the ice pillars create sliding ice tiles) and the building you can enter actually have the people inside worried about what's going on!) After running around the city and defeating a batch of grunts, they then remember that they were told the DNA Splicers could be at the Gym (you mean one of the first places you didn't search was the Gym?) and when you go to the Gym you see Zinzolin in front of it. He's easy enough to defeat so him and the other grunts run away.
Now that Team Plasma has been chased out, Drayden reveals where he hid the DNA Splicers: The Opelucid Gym (I would say that's not exactly the greatest hiding place though being that is indeed the last place Team Plasma decided to look for it...). Daryden gives us the the DNA Splicers... only for them to be snatched by the Shadow Triad! The Shadow Triad say they thought the DNA Splicers were in the Gym since they can't get in when Drayden isn't there (why not? You can teleport, how does Drayden not being in the Gym stop you from teleporting in and searching around?) and when he is there he's strong enough to chase them off. So now that they have the DNA Splicers they teleport away, though for some reason Drayden believes they're still in Opelucid City and tells us to start searching. Now we "sort of" go through the "Shadow Triad chase through a frozen city" scene in the animated trailer. Except we're not really following anyone and when we do find a Shadow Traid member it's only the one, he's just standing in front of the gate to Route 11 instead of an ice pillar, and when you battle him he doesn't have a Bisharp (though he does have a two Pawniard, though his strongest Pokemon is an Absol). Also the Shadow Traid was holding a scroll in the animated trailer and not the DNA Splicers but I understand changing that to avoid spoilers (though maybe in the games they could have had Drayden say it was hidden in a scroll). Anyway the Shadow Triad member says he was just buying his other members time to get away and teleport away himself, leaving us defeated.
Hugh and Cheren then call and ask what happened as they saw a flying ship heading toward Opelucid City (and you called me and not Drayden because...?) and after hearing what happened Cheren tells me and Hugh to go to Humilau City via the Marine Tube in Undella Town. So with that we head off, though if you want a little "easter egg" you may want to see how the ice blasts effected Route 9 and Route 11. 
9. The Marine Tube is very nice looking, it's essentially B2W2's equivalent to BW's Skyarrow Bridge. There's no items or battles you need to worry about, however if you a Wailord swim over you get a Medal however it's random when that happens and sadly it didn't happen for me. 
10. Humilau City is interesting, while Virbank City was really just another city except it had canals, Humilau City is like a resort with a beach area (where the Pokemon Center and Gym is) while the vacation goers stay in huts built on platforms over the water. Also Hugh is by the Gym and tells you to win the Gym Badge so that they can go after Team Plasma. At first you're told Marlon isn't in the Gym and to go look for him though he can be anywhere... and as soon as you go to where all the huts are he jumps out, sees you're here to battle him, and says he'll be in the Gym. But of course I first want to talk to everyone and get all the items scattered around, which for some of that you need Surf for. One interesting hut has an old woman who asks you to walk her Pokemon, a Mienfoo, and the hut and she practically yells at you for doing anything (trying to leave, looking in the trash, watching the TV...). However after walking it around enough (to see how it's doing just interact with it) and once you walked around with it enough you'll be given a Pearl.
Now I plan on exploring Route 22, 21, and Seaside Cave next so I stopped an saved here (I tried to explore Seaside Cave before but some guy with 4 Roggenrola says to come back when I'm strong enough. I checked to see if you can battle this guy and you can: he has 4 Roggenrola that are around level 40. My Emboar at that time was level 50. I think I can take care of myself).
11. Team time:
Emboar: Level 57: Blaze: Fire Punch, Heat Crash, Hammer Arm, Flamethrower
Lucario: Level 46: Innder Focus: Force Palm, Psychic, Dark Pulse, Shadow Ball
Braviary: Level 44: Defiant: Fly, Aerial Ace, Slash, Rock Slide
Amphoras: Level 43: Static: Discharge, ThunderPunch, Power Gem, Thunder Wave
Excadrill: Level 45: Sand Force: Earthquake, Metal Claw, Slash, Rock Slide
Pinsir: Level 43: Mold Breaker: X-Scissor, Thrash, Brick Break, Superpower
Flygon: Level 47: Levitate: Earth Power, Dragon Tail, Dragonbreath, Rock Slide
Going to start training Amphoras since, unlike the Flying-type Gym, I don't think Emboar can take on the Water-type Gym because Marlon uses a Carracosta which is bulky Physical wise, a Wailord which has high HP, and a Jellicent which is part Ghost-type so I can only use my Fire-type attacks which would be halved. However Amphoras should have no problem from no matter who it faces.