YJ Wrangler Door Parts
This pretty much shows all the parts in the door, even if it looks a little complicated.
For the first problem, take a screwdriver and stick it into the latch so that it is sticking out of the door parallel with the window. pull one of the door handles which will release the latch then slide the screwdriver towards the jeep. that should open it back up.
For the second problem its a little more complicated. you will have to remove the interior door panel and do a little bending and straching of parts if its similar to the TJ. Basically th door works by a small rod being attached to the handle so that it turns when the door handle turns, and when it turns, it pulls a series of levers that unlatches the door. Over time either from fatige or pulling to hard if water gets inside the door and freezes it will slip over the rod that it pulls on. Its hard to describe, but if you look at it its pretty easy to figure out. but once its sliped over the rod it is supposed to pull on the only way to fix it it to take the door apart and manually fix it.