After closing on the home, how long does the realtor stay involved with the sale? Are they immediately done with the sale, or will they remain available over the next couple of weeks to ensure everything transitions well? If it is for a couple of weeks, do I pay them more for the transition help?

The seller of the home I am buying wants to rent back for a couple of months until the house they are buying closes. How much do I charge them for rent? The exact amount of my new mortgage? More? Do I charge a security deposit as well?