Usually, only a couple of days. After the name is submitted to the register, they acknowledge its receipt by email, usually that same day. A second notification comes when the domain is completed, usually that same day or the next. Then it may take another day for the root servers to actually be updated. Of course, as soon as we set up your domain, you can access your domain immediately using the IP address that we provide you with.
Price varies between registrars.
If you already have a domain name registered, they will not charge you to transfer your domain.