Without making suggestions I will just give you some things to think about.
What ever you put here will be hard to make it water tight, so I would like to pour concrete under the door to include the slope of the walkway for a few feet away from the door.
The problem with that is this concrete should be 3" thick so it wouldn't crack. So you would want to remove some fill or concrete outside and break up some under the door.
The curve in the wall to the right, if that's the lower part of the wall thay has a curve, it was likely done when the concrete was put in, it happens.
The plastic molding around the window comes with the window and the door company just install them in a door, perhaps a door company could get you a new frame, if not they could supply a new window for that door.
You could look at making it an outswing door, that would be a different thresold at the bottom and makes the framed door 1/2 to 3/4" shorter.
I did notice the gap at the top of the door, as it looks like this door is newer than the rest of the house, so I think it was installed like that to make it fit tight to the floor which is out of level.
I would like to see a drain outside the door if possible.
BTW I agree, I would not mess with the cord wall either.
I hope some of this is helpfull.