They weren't assuming or guessing :)

You can only build temples/shrines for your own culture. If your roman, you can only build roman temples. I also think it's best in the long run to destroy the other cultures shrine as you can't upgrade it and you only take a public order hit for the 2 rounds it takes to build a temple.

The other buildings aren't culture specific so it doesn't matter. You can just upgrade them when your city reaches the next level.

Also, if none of the buildings are selectable even though you have enough cash it'll be due to your not having a govenor in that city. When you start the campain there is an option to "manage all towns" If that's not selected, you can only control the build queue in towns that have a govenor in residence. You need to dissable AI building control first.