Is he alive is the question you would ask soon after someone was close to death such as in an accident or illness situation. Example: A. He was in a plane crash. B. Is he alive? Is he living could be used when asking about someone you haven't seen for many years. I don't think I've ever seen it used without the work 'still' though. Example: A: That's Robert's boat there. The one he sold to Ben. B. Robert. Is he still living?

Was he living in a particular place

What they focus on is not different

You ask "Is he living?" when you want to confirm if he's living in a particular place. But "Is he alive?" used when you want to know he's alive or dead.

Hi Nao, こんばんは! Both can technically mean the same thing but it's more common to say "Is he alive?" if you are looking to find out whether the person still survive. "Is he living" is more ambiguous to understand without a context - it could be is he living (a good life?), is he living (in Japan?) etc. To ask whether the person is still alive, maybe you can say "Is he living or is he dead?" Hope this helps!