Is it alright to let the sellor stay in the home at least 30 days after closing? They have agreed to pay the mortgage payments. What do I have to have them agree to & sign.
This is fairly common - that the buyer moves in early or the seller stays late - but it can be very risky. Once you close, they become your tenants, and you are beholden to your local landlord/tenant laws.
If this seems like the best option for all involved, have an attorney draft up a rental agreement and hold at least first, last, and security (or more, if possible) of their money in an escrow account that they will receive upon moving out - this is to assure that they move out when they say they will. People tend to keep their promises more reliably if someone else is holding their money until they comply. You do not want to be in a possible eviction situation if their housing falls through (or if they don't pay you).
If your mortgage requires that you occupy the home within 60 days (and most do, if you bought the home representing that you would occupy it), you could find yourself in trouble with the lender if you have a prolonged tenant - even if it isn't your fault.
Check your local laws. Price out an eviction in your area, should it become necessary. Make sure that a third party (like an attorney) holds some sort of collateral and helps you draft the tenancy agreement . . . and then proceed with caution. Most of the time, this sort of friendly arrangement works out fine and allows everyone to do what they need to do . . . But once in a while, it gets very, very ugly, and you don't want to be on the wrong end of that.
Another alternative is a rate lock extension paid for by the seller. You then can close and take immediate occupancy. That avoids the landlord/tenant issues outlined in the first answer. And it is very likely that the cost of the rate lock extension would be less than market rent, security deposit, etc. to the seller. It also makes for a cleaner break with respect to your utilities, fuel suppliers, etc.
You have a lot fewer headaches if you delay the closing than you do by allowing them to stay beyond the closing date. You should also check with your lender to see if there are any documents that would need to be updated with a delay in the closing date and you should also be sure that an amendment to the Purchase & Sales Contract is done.