If you want to ask on the telephone:

is ...(name) there? can you say: ....(name) var mı?

is ...(name) not there? can you say: ....(name) yok mu?

Or should you use orada?

I think you should use orada:
(name) orada mı?
(name) orada değil mi?
or ask:
(name)le/la konuşabilir miyim?

yes, it's better that you ask the first one then you'll get something like:
evet, burada
or
hayır, burada değil
but of course they might say other thıngs like where s/he is or when s/he'll come back etc...

Yes. I had that last time I called. They started a whole story in Turkish, so I told him in Turkish that I did not understand him. But then he thought, I think, that I spoke turkish very good. So again a whole story, only about that my boyfriend was not there. But like you know, there are many ways to say that someone is not there...