Procedure to cancel Verizon FIOS and return equipment?

I am going to cancel my Verizon FIOS service (cable, home phone, and internet) and switch to another service provider. I'm not under contract and don't have to pay an early termination fee. I just want to make sure that Verizon cancels my service and stops charging me on the day I cancel. I had this problem before with another provider and was charged for 3 extra days, and I don't want that to happen with Verizon.

I would also like to know the procedure for returning the equipment. When I upgraded my service and returned defective equipment in the past, they sent the replacement by UPS, and I had to use the same box with the prepaid shipping label they provided, and take it to a UPS approved facility to send it back. Are they going to send me empty boxes and shipping labels for this? There is a large power supply unit and a backup battery unit screwed into the wall inside my closet, as well as a smaller power supply unit screwed into the wall just outside this closet. I don't want to have to start trying to take this apart and figure out how to unscrew it. Do they expect me to do that, or will they send a technician over to take back all of their equipment?

As a second question, does anyone know if there is a waiting period (and how long, if any) before I would qualify as a new Verizon customer? One of their ads says their offer is for "new Verizon FIOS TV residential customers". I would think this is meant to exclude people who already have Verizon FIOS service. Once I cancel and am no longer a Verizon FIOS customer, wouldn't that immediately make me a new customer if I wanted to get Verizon FIOS again?