OK this bit is small but confused me. How and why do they have an invisible jet on that island, and what purpose would it serve if they've been hidden from the world for thousands of years, let alone where did they get it from?
Or did they canabalize Steve Rogers plane?
I've just seen this movie for the first time, and came here to ask this exact question. I liked this movie but the one glaring issue I had with it is how an INVISIBLE JET appears out of nowhere (no pun intended) with absolutely no explanation. I'm not the kind of person who needs things explaining to them, but it's not even remarked upon. Especially given that Steve was the wise-cracking sort, and had not a single word to say about the invisible jet, just accepting it. The closest we get is him acknowledging near the end that the missiles are also invisible.
This really bothered me, and like you I'm not sure which route was even intended for an explanation. Either the jet was some ancient mythical technology (which seems extremely unlikely given the interior), or as you've suggested they somehow repaired Steve's jet... and made it invisible. Given he knows how to pilot it at the end that would make more sense, but doesn't explain why Diana can also fly the jet no problem. Or why it's invisible. The closest explanation I can think of is that it's invisible due to the silver mirror somehow, but basically everything involving the jet here was handled really badly.