Can I use an interior door frame outside, for an exterior door?
No, interior doors and their frames aren't typically primed or painted with exterior grade paints intended to protect them. Once the door and frame gets wet, it'll swell and stop closing properly. Then the door will begin to rot and fall apart because many interior doors are made from pressed sawdust, fine wood pulp and heat sensitive glue.
How do I know if my door needs jack studs?
Whenever you're building a door frame, jack studs are required. They add strength and structural stability to your door, and if you don't use them, over a short period of time your door will not function properly.
How do I attach the floor plate to a tile without tearing up the floor?
I would recommend removing the tile anyway just for completeness, as well as for the minuscule amount of head room (sometimes every bit counts). As long as there's concrete underneath the tile, you can use a hammer-drill to make a hole that will go through the tile and the concrete, or if you want to be careful, drill the tile slowly with a normal drill, then hammer-drill, then anchor the plate to the floor.