A concrete footer must be poured around the perimeter to support the coping stone. That's the correct way.

If it's laid directly on top of the pool panel, it will rock and come loose.

Granite is a very hard and durable material. A textured surface is best to keep it non-skid. Pavers are just fine.

I see no issues in regards to salt with either material.

If you don’t mind me asking, what should this footer look like in regards to size - width and depth?

Generally 12"-14"" deep with a row on top and the bottom of 3/8" reinforcement bar (rebar). This will help prevent any deflection in the concrete during the freeze/thaw climates where it can move. It's good practice to reinforce the concrete anyway no matter where you live.

BE SURE THE REBAR IS PROPERLY BONDED TO THE POOL STRUCTURE.

Whatever the width of coping (measure front to back), the pour should be 2" beyond the overall width when it's set. In other words, a 12" stone with a 2" overhang, requires a 12" base. Since the stone will sit on the pool panel also, which is generally 4", the actual concrete pour will be 8".

I see alot of guys pouring 6inches. Will that eventually move?

In freeze/thaw areas, absolutely.