Yes, the Finder UI is fundamentally now a Cocoa app.

However, internally Finder still uses many of the same Carbon file management APIs that it always has, simply because there still are no reasonable equivalents in Cocoa.

Many Carbon APIs are still part of the Snow Leopard SDK and are available in 64-bit for that reason; the hot key API is one example.

Yep, it was rewritten in Cocoa for Snow Leopard:

http://arstechnica.com/apple/reviews/2009/08/mac-os-x-10-6.a...

Yes it has. They rewrote it for Snow Leopard (but they didn’t change anything about its functionality or looks).

Basically everything is Cocoa in Snow Leopard with the glaring exception of iTunes and it's really starting to show, they really need to do a rewrite. Hopefully they don't call it iTunes X like they've done with the Final Cut and Quicktime rewrites.