Unless I have missed something along the way, you can lease a domain name. The current structure that is in place allows you to maintain control over a domain name for periods of time. You are not able to buy a name for ever.
Much like an IP address you don't own an IP address, you have rights to use the address but thats about the extent of it.
One of the biggest things to remember is that you are not stuck with the name nor does it have to be hosted specifically by any one company or ISP. I personally use
http://www.godaddy.com/ for my domain purchases and have had great service. You are able to change name server host addresses renew your domain lease and much more from the web interface. If you decide to sell your domain rights, they also provide the means for domain transfer from one entity to the next.
As far as a certificate, I guess that would depend on the company that you lease through. I received an email and that was about it.
Hope that helps.