Translation:Is your father tired?
"...te iru" is stative, that is, the action is the current state of affairs. That can mean either that the action is on-going or that no further developments have happened since the action was completed. The usphot of that is that depending on context and semantics, it can be translated by the English present progressive or past perfect tense. (Tegami ga kite iru = "A letter is coming" or "A letter has arrived."
It depends on who is talking and to whom he is talking.
He could be talking to a member of his own family circle, all of whom would call the father "otoosan," and, in that case, be talking about the father of his own family.
He could also be talking to someone outside of his own family and, in that case, be talking about his listener's father.
Presumably, he is not talking about his own father to anyone outside of his own family. (But I'm not sure how well the old conventions are holding up these days.)