From reading the below link, the way I understand it is that if you pay off 100% of the balance of the device it's yours to keep but you can also trade it in for the trade-in value towards a new device. If you want to do an Edge-Up early without paying off 100%, you have to pay up to 75% (depending on when you entered your Edge agreement) to be able to change phones.
I don't personally use Edge but I know a few people that do. If I'm incorrect, please correct me.
You can pay your balance any time you wish...and the phone is yours to keep. You can trade it in when you decide to purchase a new device and use the trade value as credit...or you can keep your phone and sell it via other avenues.
Depends on when the Edge agreement was created. Those new rules go in effect for agreements signed after May 31, 2015.