For the Polter sword/armor/helmet you want to equip Talismans to save your characters from instant death from destroying the Sword or the Rainbow Earring prevent status effects. Also they are Darkness based so having Miranda throw Light based magic at them will do a ton of dammage but she will also take extra dammage so have healing stuff on hand and maybe an Armor of Legend. Rose is handy to have in this fight because she's got great defence against Darkness based magic with her Dark DS Armor and Roses' Hair Band to prevent instant death.
The Dragoons are Earth, Air, Water and Thunder based. You might want characters that are the same element who take less damage and ones who are the opposite to do greater damage to fight them. If your Dragoons are wearing their elemental armors, they take way less magic damage. Both Earth & Air are weak magically and strong physically so you could have a strong magic user take them down pretty quickly. For the Water based Dragoon, Meru is great for taking little damage and Dart for doing major damage. For Kanzas the Thunder based Dragoon, you probably want Hashell and another character who is fast, well armored and balanced between physical and magic damage because he can do nasty damage with both. He's one of the harder fights in the game.
To fight Faust, you need to have collected all 50 Stardust to get the Vanishing Stone from Martel which destroys his magic doppelganger. After that, equip Legendary Casques, Angel Scarf, Phantom Shield, Spiritual Ring: anything to cut down the magic damage he does. He will not attack physically so max out on magic defence. Also added speed is handy to try and slow down his multiple turns. Do NOT attack him with magic, stick to physical attacks. His counter attack after you hit him with magic does massive damage and often kills with one spell. He often attacks with the same element as one of your characters so getting the Elemental Armors is a big help.
You won't be able to fight the 4 original Dragoons until after you speak to "Emperor Diaz"/Zeig/Melbu Frahma. Until then the spirit of Shirley keeps them inert. Once you've spoken to him, crossed the desert and dealt with all the stuff in Ulara, you can go back and fight them anytime you like after that.