No response from professor for letter of recommendation
If you are able to, you might consider attending office hours if your professor has them openly available before the deadline. In the event that your professor misses this first deadline, I would try to get them to submit the letter to the other schools as soon as possible. It is likely that all of the letters will be basically similar (meaning that all letters should be already written), so an early submission to the other schools should not be an issue.