When you get all the spells powered up to Gas you get the dream rod for Donald, not the dream sword for Sora (you get Stopga by beating the phantom, read the CHU FAQ's for the Dalmatian locations)
You can re equip your characters after the fight with the first Ansem, give Sora Elixirs, the fight with Ansem is the same as the last one, he has new attacks but you can either dodge them or heal in between his attacks (when the Demon starts popping up out of the ground, lock on to Ansem and run around him in large circles and you won't get hit).
You don't have to beat Cerberus yet, come back there after you beat Deep Jungle and Wonderland.
To find the third district, I think you need to go back to the first district and talk to Cid, other than that when you go from the first to the second I think you take the first right after you go down the stairs
To get the Ultima Weapon, you have to synth all other items first, you get the mystery goo from the mushrooms, when you find white ones you need to use a spell on them based on their mood, if they shiver, use blizzard, if they fan them selves, use Fire, Floating = Gravity, Spinning = Aero, Begging = Cure, under a sun = thunder, each mushroom needs 3 spells and if you get all three the same they almost always drop one
Ragnarok's impact shoots lasers that home in on enemies that fly
I'm not sure which treasure chest you're looking for in HB, you can only get to a few of them after you beat it for the first time, and check the FAQ I posted about 2 pages back.