Civilization – way to tell which spaceship parts the other civs have built

Sounds like you were unfortunate to not spot the issue earlier; probably the best thing you could have done at that stage would be to fortify your borders, hope to deflect the first wave (when it eventually comes) and then counterattack, charge in and capture and hold a few of their cities (thus making them weaker). Although if you were aiming for a cultural victory you would need to avoid annexing any, otherwise this will make your social policies cost more.

In my experience Montezuma and Augustus are, by default, quite aggressive when played by the AI; if you find an AI playing either near to you, I feel it is best to plan ahead to stop them expanding too much and have sufficient defence on that border - or instead try to make sure you get friendly with them so they're on your side instead.

Also, I believe entering in to a pact of Secrecy with other Civ's against a threatening Civ earlier in the game would have helped prevent the other Civ's becoming allies with the threat later on, by ensuring they have a "bad" relationship with the threat. But I don't have hard evidence for this.

I can confirm a very good effort for a science win from AI. They have built an Apollo Program and several ship parts. It was a really nice end-game race, as I was beelining tech tree to rush United Nations for diplomatic. It was my first successful immortal game so I didn't want to lose it just to see if AI can win, but it certainly looked like they could.

On the other hand I had another game where I was hopelessly lagging behind a runaway AI on science. They entered future era, when I was still in mid-industrial. But they were so busy conquering the world that didn't bother to go for science victory. So it might be that if AI is set up to achieve dominance they won't go for other types if victory.