Do they allow people to be able to live in apartments for how ever long as that person wants/need if they pay?

As long as you pay generally as long as you need/want to. Sometimes buildings change hands and there is a change to condos or something and the owners will ask you to leave. Or they're planning on levelling the building so you need to move.

I bought mine so I can have it forever - or until I die, whichever is soonest!