It's a rather flimsy door of thin sheet metal and glass that you often see on the outer side of a house door. In the winter, it provides a layer of dead air space that helps to insulate the house. In the summer, storm doors are often fitted with screens to provide more ventilation while keeping insects out. This is still common today, but was much more common before air conditioning was ubiquitous in the US. BTW, storm windows are also a thing, and are still common in the US for the same reasons.
I think you're looking for a storm door glass retainer. This does not look like weather stripping to me. Generally , weather strip goes on parts that are designed to move and need to seal (the soft black plastic around car doors). If it's soft and pliable, it's probably weatherstrip; if it's rigid and inflexible it's likely glass retainer.
I'd follow Decoy321's advice and take measurements and pictures, then go to your nearest hardware store. But odds are they won't have the exact match for the existing door, this glass retainer is generally unique between manufacturers and even within product lines.
You may have better luck going through a window and door installer and see how much it would be to get them to repair it, since the parts are so unique.
You’re correct, and to make things worse this door manufacturer went out of business about a decade ago. I may just drill some holes in the door and use regular storm door clips to hold the glass. Ugh!
If you're particularly handy and not particular on perfection you could try removing and reshaping it. Heat gun and some clamps could do wonders. If it cools or sets a little long, trim to fit. Too short, caulk.
I believe it's called a mullion. It is a hard plastic strip that snaps into a groove to lock the window pane to the door frame. They can be purchased but they have to be the exact size and profile which can make it difficult to get. You might be able to work it back into the groove and snap it into place.
It just looks like a sealant. It keeps the glass panel fitted to the door frame.
First, get the measurements of your door and that sealant (x" by y"), then take that number and this photo to a nearby hardware store. Show someone the photo, and they will most likely recognize it and be able to help you.
Insect screen kits is what you might be looking for. I am guessing there may have been a screen net in this plastic frame at some point. You can always buy the net separately, but not 100% sure about the frame it's self.
This is called glazing bead. It's used between the door and the surface of the glass to hold the glass in place. You might be able to find a comparable replacement at a window supply or aluminum warehouse that services glass in doors and frames. Good luck!