Domain registration is entirely under your control. You will get a domain control panel for free. You pay when you register or renew a domain. You have full control on your domain, you can transfer your domain anytime you want. Domain is registered in your name. You can change name servers to any name servers of your choice.
Also, domain registration and hosting services are separate. You can have one or both.
When domain registration is paid for by paypal, registration is immediate. When you pay by 2checkout, we wait till fraud check email from 2checkout, which may delay it for 12 to 24 hrs.