How to Replace Exterior Door & Casing in Old House
The basic procedure for removing a door is: remove casing, remove screws from jamb/brick mold, and push the door out of the hole, brick mold still attached. Unfortunately your situation calls for some more devious tactics. Because the outer molding appears to be part of the transom casing (assuming you're leaving that part alone) you're probably better off not disturbing it. So you have to remove the interior trim, remove any screws that connect the jamb to the substructure, then very carefully prize the jamb away from the outer molding with a bar such as this:

to keep from marring the backside of your brick mold.
Once the door is out, the problem then becomes finding a new door/jamb that fits the opening not just properly but perfectly in order to get the reveals right, which may be a challenge considering how old and...unique your existing door is. If you over come that hurdle, just caulk the backside of the brick mold with sealant (sealant not caulk) and follow the manufacturers instructions for sealing the threshold and all should be well. Cheers!