How do you attach a model inside a shadow box without it sagging over time?

Yeah, glue dots sagging is totally normal. They're basicly soft adhesive and they creep under constant load, expecially in a warm room. What worked for me was taking the weight off the glue entirely. I drill a tiny hole in the felt-covered backboard where the stand or a support rod goes, push a piece of brass or steel wire thru it, and glue that to the back of the board. The rod carries the model, the glue just stops it sliding around. If you don't want to drill, even a small bead of hot glue or a construction adhesive blob under the belly works fine because then the glue is in compression instead of being peeled apart. The failure mode with dots is peel, and peel is exactly what a nose-heavy jet in flight pose produces.

I'd push back on the hot glue suggestion. Hot glue on a painted belly is a bad idea, it grabs the paint layer and when you eventually pull the model off the board for a repaint or a diffrent box, it'll lift paint right off with it. Ask me how I know. A construction adhesive blob is even worse since you're never getting that apart cleanly. If you're going the glue-in-compression route, at least put a small square of wax paper or a smear of vaseline between the glue and the model so it releases later. Also, on the sunlight thing, that afternoon exposure is enough to fade decals within a couple years in my expirience, so I'd move the second box.

For the sunlight question, I learned that one the hard way. Had a 1/48 Corsair hanging in a hallway where the afternoon sun hit it, and within a year the decals had yellowed and the red on the tail went pinkish. What saved the rest of my displays was a roll of UV filtering film stuck on the window itself. Cheap stuff, barely tinted, and it made a real difference. An hour or two of direct light a day is exactly the kind of spot I'd film before hanging anything I spent forty hours painting. Paint alone might survive, but decals fade fast.