Boarding starts 35 mins prior to departure on narrow bodies and 50 on wide. Everybody sticks to this rule pretty well unless there are a lot of wheelchairs or other special needs customers in which case we might start 5 mins earlier.

CO will allow early push backs but no more that 10 minutes and only if all pax are on board. 20 mins seems unbelievable. Haven't pushed back that early ever.

Yes, I think gate checking bags, to be brought up to the door on arrival, would be impractical. It works for smaller planes but there are many fewer pax. With a fifty pax plane there are never 50 gate checked bags.

FA's do try to close OH bins in F for boarding but they get opened as soon as the first class pax start coming on board and they generally don't close them unless they are full. They do try to monitor bins during boarding for someone blatantly placing their item in F when they are in back. Does happen sometimes though.

Gate agents can get in a lot of trouble for closing late if it's their fault (up to termination). That's why they are always kind of panicked when it gets to closing time.