Storm door on odd sized frame
There's nothing wrong with screwing the door to those two lips on either side. Depending on the weatherstripping on the bottom of the door, it should fit right up to the cement bottom, or top of that sill. Adding an additional "header" piece should not pose much of a problem. It could even extend a bit below the existing one if necessary for a good fit. Hardest part will be cutting those two angles. A saber saw will do the trick if you don't have a miter saw.