It's also a lot faster to refuel a plane than to recharge those enormous batteries. That's longer turnaround times between flights, huge(r) delays if you need to stop to refuel due to weather, etc.
That can be mitigated by using modular batteries designed to be easily replaceable during any stop. Land, open the cargo bay doors, remove battery modules, add battery modules, take-off. This sort of operation can take far more time than unloading luggage due to the advantages of using standardized containers.
Depends, it takes about 20-30 minutes to start a jet; do all the pre-flight checks, etc. Add to that boarding, cleaning, etc. and most planes would be on the ground for at least half an hour and probably closer to an hour in between flights. That's plenty of time to recharge.