I live in an apartment with my parents that pay for the rent, do I count for this "Rent or property tax for your principal residence in Ontario was paid by or for you"?

Yes, but you can only claim the amount that you pay for your share of the rent.

I'm looking at the list of Manitoba tax credits in provincial section, not seeing a place for rent. The closest thing is education property tax but it does not provide me a place to enter my rent paid.