What happens when you lose a city after you have built the forbidden palace, bringing your total amount of cities under the number that is required for the FP?

Nothing. That is only an issue if you are building it at the time you lose the city. (EDIT: Plus, it remembers how many hammers you put into it if you restart it later - although this amount deteriorates after a certain number of turns, I think it is 50 for buildings at normal speed).

... First of, why is this in the Strategy forum?

Nothing. That is only an issue if you are building it at the time you lose the city. (EDIT: Plus, it remembers how many hammers you put into it if you restart it later - although this amount deteriorates after a certain number of turns, I think it is 50 for buildings at normal speed).

I believe it's 10 for units, 50 for buildings, maybe even more for wonders, if they are not build by others.