can I use an antique door outside?

You can, provided the timber is thick enough and built for external use. Solid oak or heavy painted pine examples survive weather well if properly maintained. Interior doors aren't usually thick enough for exterior frames. They often warp when exposed to rain on one side and central heating on the other.

we just moved into an old house and the original internal doors are coated in this really thick horrible paint, should we strip them or just paint over it again?

Stripping thick paint usually reveals the original crisp mouldings that decades of redecorating have obscured. It is a messy job, but uncovering those sharp joinery details transforms the look of a room. Pine doors were often meant to be painted from the start. You might find rough timber underneath, so be prepared to prime and repaint them rather than leaving a bare wax finish.

what size are old doors?

There isn't a standard size. Local joiners built them to fit individual frames and specific room proportions. Measure your opening twice. It is easier to trim a larger door than to build out a small one.

I found a matching pair of huge double doors from a church but they seem too tall for my hallway, is it okay if the carpenter cuts a bit off the top and bottom?

Trimming is normal, but taking too much off will ruin the structural integrity. The joints connecting the horizontal rails to the vertical stiles rely on the timber at the top and bottom corners. Cutting too deeply removes the tenon pins holding the frame together. You'll also risk ruining the visual balance of the panels. Consult your joiner before buying. They can tell you how much tolerance you have before the frame starts to weaken.