I have a question: Does the fact that पिता ends in ा mean that it is singular, and that if it were पिते, we would be saying “fathers”? Or can पिता be translated as “fathers”? I am confused because it is a typical masculine noun, and by the earlier pattern, I thought it should be switched to end in “e” any time we actually mean to say “fathers”. I understand that we should use तेरे and हैं plurals for respect either way.
Yes I think you'd achieve that with आप के। Everything else the same.
Or आपका ।।। है if you wanted to remove respect to the father at the same time.
Also bear in mind that you don't know you're talking to a man here, the gender of the personal pronoun, whichever you choose, is agreeing with their father, not theirself.
tere (तेरे) is very familiar (rude if said to someone you don't know)
tumhare (तुम्हारे) is informal/casual
aapke (आपके) is formal/polite
You can use any of the three depending on whom you're talking to.
There is not "there" or "thumhare". The consonant is /t/ त - an unaspirated dental voiceless stop.