1.
it doesnt real matter, you eventually ge key spheres which unlock those spheres but just follow the path that seems natural to the character.
2.
it is possible to get all abilities for every character if you complete the whole sphere grid.
3.
you can return to every location and i dont think theres anything 100% unmissable but be careful if you have the english version because there are dark aeons gaurding certain locations. dark aeons are superbosses and wil take a lot of leveling to beat.
4.
id reccomend that you do so. because some parts of the game force you to use certain characters and it would make things a lot easier for you.
5.
the weapons arent like on other FFs and the only way to make yourself do more damage is by raising strength or getting something like strength +10%.same with armour. the only weapons that do extra damage without these things are celestial weapons. there is one of these for each character and they are very hard to find and power up so i wouldnt focus on them yet as they are unecassary and will only be needed for certain superbosses(not 100% needed but they are reccomended.)
6.
gil is just like in the other games(apart from FF8.) monsters drop it and you use it to buy items and weapons and various other things.

i hope you enjoy the game.
BTW. youve been on this site longer than me and this is your first FF? youve got to buy the rest because in my opinion this is good game but games like FF8 and 9 and a lot of the old ones are better still. i hope you become a massive FF fan like me and try as hard as you can to get every FF.