Sql server is 'nothing' more than a windows service. By owner of instance, perhaps you mean the account under which the ms sql server service is running? If so, manage computer, services, choose the service with the instance in question, set the logon name & password.
Your .Net apps --> depends on "how" they are configured now. If they are on the same box and were using something like (local), nothing need be changed. If they were configured to point to the machine name, such as machine.old_domain.com, then simply changing them to machine.new_domain.com. If they are configured to point to machine and the name of the machine didn't change, no configuration changes needed.
This are just starter answers. I've never had this happen to me. Good luck my friend.