Might be easier to install the same size door or the biggest one you can. They are pretty simple to install especially if the hole is already cut. If you go bigger you will need a sawzall and a long drill bit and caulking.

It could be fixed but check if a 2x4 support was cut, might think about adding something back in, then the insulation and interior wall would be easy.
Exterior I would add flashing and the black tar paper, then its more cosmetic after that if you want to piece in a few boards that look the same and paint to try to hide the seams or put in new across the bottom to hide seams.

Lowes or home depot can match paint no problem, just take in a chip or sample. They can make you a sample size can to test out which would probably be more than enough if you patch the hole.