You can play up to 5 tribes at once, since there are 5 player slots in the game. Each tribe operates independently of other tribes; you can set the speed of each tribe (or pause it) without affecting other tribes. Switching from one tribe to another 'quits' the tribe you switched out of, but time will continue to pass at the speed you've selected (unless it's paused).

As for 'messing with the clock,' you may find this answer in our Support FAQ helpful.