Black and White lock the main story to Unova-only Pokemon. 156 new species with no old Pokemon until the postgame. Every evolution chain you encounter is new. Trade evolutions, stone evolutions, and some new methods like leveling with a specific party member (Shelmet and Karrablast) are all present.
No. Black and White restrict the regional dex to Unova-only Pokemon until you beat the Elite Four and unlock the National Dex. Every evolution chain you encounter during the main story is from Gen 5. This was a deliberate design choice to make the experience feel fresh, like playing Gen 1 for the first time.
You trade them for each other, specifically. Trade Karrablast for Shelmet and both evolve simultaneously during the trade. Karrablast becomes Escavalier and Shelmet becomes Accelgor. Neither evolves if traded for anything else. It's the only mutual trade evolution in the series.
Gen 5 didn't add many totally new triggers, but it did some creative things with existing ones. Karrablast and Shelmet's mutual trade was a first. Mantyke evolves when leveled up with a Remoraid in the party. And some Pokemon like Eelektross have unusual stone requirements that catch people off guard (Thunder Stone for Eelektrik).
Gen 5 introduced 156 new species, the most of any generation. That includes complete new three-stage families like the Deino line, the Litwick line, and the Axew line. No cross-gen evolutions though; unlike Gen 4, no older Pokemon got new evolved forms.
Larvesta evolves into Volcarona at level 59, the highest level requirement of any non-legendary evolution in the series. You get a Larvesta egg on Route 18 that hatches at level 1. Getting it to 59 is a real grind, but Volcarona is one of the strongest Bug-types ever made, so it's worth it.