I would use the present tense "come from" to talk about a general sense of coming from and growing up in a place. I am from Australia. I was from Australia yesterday and I will still be from Australia on the day I die. Therefore I can always use the present tense to talk about coming from my country or city. "I came from" in the past tense implies a one time situation that has now finished completely. For example, I came from the shop to this location. I don't have an ongoing connection to the shop, and the action is now complete. If you were to say "I came from Australia", it implies that it is a one-time situation. For example when you cross a border you could say that you came from the other country. In this case it does not carry the meaning that you grew up or spent a lot of time in that country. https://english.stackexchange.com/questions/103152/i-came-from-italy-or-i-come-from-italy https://www.englishforums.com/English/CameFromVsHaveComeFrom/pxpkp/post.htm

come from, because it's your origin which doesn't change

The other answers are correct, talking about your place of origin you would use the present tense, come. To answer the second part, about a similar sentence with your parents as subject, the tense would depend on whether or not they are still alive. If they are then use the present, if not then the past

I come from...

I come/hail from