1) It varies from registrar to registrar. Basically, use the transfer feature in your registrar's account where you want the domain to end up. The domain's owner will then have to provide the authorization code (also known as "transfer code" or "EPP code"). Then just enter the code in your account, and the domain is yours.
2) I can't comment on the registrar you're looking at using, as I'm unfamiliar with it.
3) You can use any host you want. They should have instructions for getting your domain set up after you get it transferred to your registrar account.