Do I really need to replace all gears in my diff?
 

I had a knocking noise in my rear area whenever I coasted. If I stepped on the gas it would stop if I braked decently hard it would also stop until I took my foot off the brake again. I took it to a large shop and they said it was the differential knocking. They said they wanted $350 just to take the gears out. Mechanic said that there was to much freeplay with the carrier set and freeplay in the ring and pinion. They basically said the whole things needs to rebuilt and that parts and labor would cost about $2,600. Does the entire thing need to be rebuilt if thats all that's wrong? Should it cost this much? Can I take it to the ford dealership this time and have them take a look? The shop said that they still have all the gears.

$350 to take apart the rear end complete isn't to bad, I'm assuming labor rate of $100-$130 an hour.
Without pictures its basically impossible to say what all needs to be replaced in the rear end.
Rebuilding a entire diff can be rather expensive, if you can do the work yourself you could buy a scrap yard diff and swap over the internals.
Honestly if you take it to a dealer already taken apart we're probably just gonna say to replace everything since we didn't get to see/feel it for play/wear.

It turns out I have 1 year of powertrain warranty from the dealer I bought it from. I found it in the contract I signed. Do you think I am going to be given problems if I bring him the car with the differential apart? Do you think he is going to put it back together or demand that I put it back together before he fixes it? Have you heard of dealers trying to not honor the powertrain warranty for a reason like this?

I'm not sure, you could call your dealer and ask them, the issue for the dealer warranty is we can't feel the issue because its already apart so we can't definitively fix it first go around and the off chance that a part is now missing or damaged from disassembly you would need to pay for said missing or damaged parts.
Its possible you may have shot yourself in the foot by not taking it the dealer.