Civilization – Does a colosseum create 2 happiness or 4

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.

The base number of turn for the Taj Mahal is 15 a turn Golden Age. The Chichen Itza world wonder will increase that number by 50% (= 22 turns).

Building the Taj Mahal as Darius resulted in a Golden Age of 33 turns (should only be 50% longer). Darius with Chichen Itza resulted in a 49 turn Golden Age.

The base value seems reasonably balanced to me, maybe a bit too powerful. With Chichen Itza it is very powerful, but Taj Mahal with Darius is just outright overpowered, or even broken.