The bottom would be easy enough by making a curb on the inside of the door frame. Essentially, the door would close flush into the vertical "wall", but there would be a jamb inside the wall. Think of how one of your home's doors closes against a jamb. You could do the same thing at the bottom. 2" high would probably be sufficient. A rubber/foam gasket would help, too. It'd certainly stop rainwater - and probably 99% of any 'huge' rush of water.
Nah, your picture is perfect. And now I see what you're getting at. BUT... looking at the picture of that Marlin, it does not appear that opens "completely" like you want to do. But you could still do what you want and I don't think you'd compromise and rigidity of that area. However, if it was me, I would leave a good 2" of that vertical wall - in other words, start the "hole in the wall" about 2" above the floor. Doing that, you'd probably only need a 1" jamb. I'd do the jamb around the bottom edge of the hole, and also the two sides. That way when the door is closed, it nice and solid and won't accidentally pop inwards if you happen to bump against it. The top edge of the door and the "lip" of the existing hatch can be relieved to fit into each other (and keep rain out).