It's not possible to get a user's owned games except through the WebAPI.
You can get some profile details from steam-user.
All you can get from steamcommunity or the WebAPI if a profile is private is their name/avatar/basic info. You can get profile info from steam-user's getPersonas if their profile is friends only and you are friends, but there is no way to get a completely private profile.
Yes, you can change profile privacy from steamcommunity.