Screen hinges experience extreme loading in a non intuitive way because they are in such a small form factor and the leverage ratio that creates. Laptop hinges are very engineered. I don't expect great results from a general repair consumer epoxy.

I can't see the issue (yet). I am a pro automotive painter, or was for many years. Do not use adhesive , especially super glue or tape.

If you have all of the pieces, that are missing, and you can get the thing apart with access to the back side of the part. It is possible to use a soldering iron set to a low temperature to plastic weld the thing back together. I can reconstruct automotive trim like, accents, mirrors, handles, and bumper covers even when they look crunched or are in pieces, so long as I have all (most of) the pieces. That is a little different because I am totally refinishing the parts, but I have put other stuff together to make it as good as possible. The trick is to put everything back and as tight as possible, then use the tip of the iron to mix the plastic melted on the back side. It is best to have some filler material of the exact same type to add into the repair. I usually get this from obscure hidden areas of the part. Getting the heat and temperature right so that the front of the part is never overheated is a skill. I usually also embed a tiny fine metal mesh across the back side of the crack, embedding it just below the surface. Localized heating will make the spot more brittle. It is best to use a heat gun to try and anneal some of the stresses, but it isn't required. ABS like plastics work best. The only thermal plastic that I know of that does not work with plastic welding some forms of polypropylene. Almost all common plastics can be plastic welded for repair.