Yes, both work. Gmail has filters. There's no way that I'm aware of to import from Evolution (or any other client (but I haven't really looked very hard...))
Assuming you own the domain name and have it switched over to the Goog for mail, you can have up to n (last time I looked, n = 10) named email addresses, each with their own account/password/etc...And you can also have a catch-all that delivers everything-else@domain.com to the catch-all. I make heavy use of that since switching from running m'own Exim to Gmail.