I am selling my home on the 8th of the month, should I make my mortgage payment due on the 1st?
It depends. Many mortgages have a grace period between when the payment is due and when it's late.
closed on a house, when is my first mortgage payment
When is my first mortgage payment?
For most mortgages, the first mortgage payment is due on the first of the month that's 30 days after the closing date.