Congrats on jumping in!
Regarding the utilities do you know what utility companies services the house? If you are supposed to pay utilities or the tenants? You will most likely at very least be paying for the water/sewer so I would start there by calling the water company in the area and transferring the account to you. Depending on the other utilities call the rest of the companies and transfer the accounts.
Regarding the back door you may need to get a lock smith in there to switch out the lock, which should not be very expensive.
When you handed the tenants the letter stating that you took over ownership did you discuss the move out date with the tenant in the unit to be vacated? if not, you may need to go and physically knock on the door to see what is happening in there. Make sure you have a working number for all of the tenants and keep an open dialogue with them of their needs and issues.
Good luck and let us know how it goes!