Ape Apps

are embassies an actual building you can place down? or can you not place an embassy in another one of your colonies?

A embassy is a placeable building. And you need to place it to get the embassy shown in your Embassies.

what section would it be in?

Embassies are not in build menu. You can only build them if someone sends it to you. When you receive an embassy, a blue handshake button pops up next to the inbox button at bottom right of screen. All the embassies that you have got and haven't placed can be seen there and you can place the embassy only through that button.

Exchanging embassies is a good way to increase contact and stay in touch with the colonies that you like or have helped you. So it's recommended to have them with lots of folks.

so i presume you can't put an embassy from one colony of yours into another that you own?

Only independent colonies can send and receive embassies, doesn't matter if they are yours or from someone else.
If you are in a commonwealth as a member, not as the owner / or under United Earth, you cannot send or receive embassies.