Its all about trust ya know?
Yes all of the above is possible
Its even possible to have ONE domain for both sites (believe that is the MS recommendation for AD but depends on your needs)
You can put both 'Trees' in the 'Forest' and they will trust each other...
Sounds like you should do some serious research on Active Directory before starting it up though.
Yes users can use Exchange from across remote sites
THINK about security though!!
If you're going to be doing ANY of this USE a VPN!
You do NOT want all that traffic going across the internet un-encrypted
If you ask what a VPN is, you REALLLLLY need to do some research on this
We can only help so much, but when it comes down to it, your sites security is relying on you... not some folks in a forum.
hardware
prices 
