B2W2 mixes old and new Pokemon from the start, unlike the Unova-only restriction in Black and White. Eevee, Riolu, and Magikarp are available early alongside Unova originals. Same evolution methods as BW, but wider access to chains means more team options during the story.
All seven Eeveelutions available at the time are obtainable. Friendship during the day for Espeon, friendship at night for Umbreon. Fire/Water/Thunder Stones for the Gen 1 trio. Level up near the mossy rock in Pinwheel Forest for Leafeon, or the icy rock in Twist Mountain for Glaceon. Sylveon didn't exist yet, so seven total.
Not exclusive items per se, but version-exclusive Pokemon mean some evolution chains are easier in one version. Black 2 gets Magby and its evolution items more readily, while White 2 gets Elekid. Both can trade for the other, but completing the full cross-gen evolution set is faster if you have both versions.
The Memory Link (connecting to a completed BW save) unlocks flashback scenes and a few extra encounters, but it doesn't significantly change which evolution chains you can access. The real difference in B2W2's evolution availability comes from the expanded regional dex mixing old and new Pokemon from the start.
Funfest Missions in the Entralink can reward evolution stones early on. Dust clouds in caves also drop them randomly. The PWT (Pokemon World Tournament) area vendors sell some. If you need a specific stone fast, check dust clouds in Wellspring Cave, which is available before the second gym.