You will be signing a contract with the buyers before they give you money! Their initial deposit will be held in escrow until the closing.
There will be contingencies in the contract that have to be met....like home inspections, and most likely one for a mortgage contingency...perhaps an appraisal contingency, too.
The mortgage with Wells Fargo will be paid off during the closing. Final numbers and calculations will be given to you by the title company or attorney just prior to the closing (and, in case you ar upside down on your mortgage, and you need to bring money to the closing table to pay it off - those figures will be given to you then , as well). The mortgage payoff figure is calculated per diem up to the actual closing date..
A new deed will be prepared.... and recorded for the new buyers following the closing.....you don't "wait for the deed" from Wells Fargo).
Are you familiar with your local C of O inspection requirements?.... or arranging for final utility readings??
There's a lot more to a closing than just paying off the mortgage!
Since you are not working with an agent, and are CLEARLY in the dark as to what to do regarding the home selling prcess........turning to a RE attorney is probably an excellent idea.......and a prudent place to start.