Can a bus leave a scheduled stop early?

I guess that would depend on the transit company. Here in St. Louis, the driver waits if he is early. That's what schedules are for.

This depends on the transit company. Some companies monitor their buses very closely so the system will realize that a bus is leaving a stop early and then the dispatcher will call the bus driver to tell him to wait for some time. Other companies have no idea where their buses are so nobody is monitoring the drivers. Anyway, to gain a good customer satisfaction, a bus should NEVER leave a stop early, thats what timetables are made for. So if this happens on a regular basis you should contact your transit company and make a complaint. It will help if you can tell them exactly at what time the bus left early. This will help them identify the responsible driver on that bus. Keep in mind that there are situations that might seem to the passenger that the bus is leaving too early when it's not. For example if the buses are running late and the bus you see departing at 1:19 is actually the one that was supposed to depart at 1:12 (7mins late) and not the one at 1:22 (3mins early).

It depends on the rules for that company. Where I live, they are allowed to leave up to 5 minutes early, so people are supposed to be at their stop 5 minutes before the stated time.

They cannot leave early from their starting point or their layover spot (bus waits to connect with another route). Timepoints are main stops along the route that are used to estimate arrival time.

that bus could be late you could be seeing a late bus and you are assuming its the 1:22pm when it could be previous bus

It is driver's discretion.