I think about creating a Stack Exchange site. My friend owns a domain with appropriate name. Is it possible to assign a released site (when out of beta) to a subdomain? If yes, how can the owner of domain control data on that site?
No, that isn't possible. All Stack Exchange sites are the property of Stack Exchange, and are usually hosted on a subdomain of
subsite.stackexchange.com. There are relatively few exceptions, the only two I can think of being stackoverflow.com and askubuntu.com
If you want to run your own Q&A site on your own domain, there are open source clones of StackExchange you might want to look into.