I wish you were local, i'd help you! You can do it.
Take off the old one and reattach like it came off, with same type harware.
Make sure to seal the gaps.
Ditto...If I had any time to catch my breath I'd at least come look at it and give you a pat on the shoulder. LOL.
As long as the foundation/mounting surface is intact, You can do it....
Looking at your pics...it actually doesn't seem that bad. A wire brush, sandpaper, paint, caulk etc....It will be as good as that setup can be.
Wire brush and sand the thing, repaint it. Buy some generic rolls of wide weatherstripping and run it on the inside of the doors where the door meets the frame, strip away all the old caulk where the frame meets the concrete and re-caulk. Weekend project!
You are probably getting as much leakage from the concrete structure as you are the door too...might look at some sealant inside.