Changing Grand Companies

[Felis]

If you change nothing get reseted. Your progression in the old GC get saved and your progression in the new GC get loaded. If you change to the new GC the first time then yes, you start at the starting line.

I highly doubt this would happen, because what if your inventory is full? Would you get the "Unable to obtain ______" message? That would be poor.

the same what happen if you have job specific gear on (like AF) and you want to unequip your job crystal while one of your armory chest slots is full.