I main fire too. The game does not have many good healers; I think only Water has more than one good healer right now. Fire has the SR Brynhild, which heal 1200 at max level. R Konohana-Sakuya heals 500 and reduce enemy attack, maybe one of the bests R of the game. What Fire has is a good quantity of regeneration/energy drain (SR Sun Quan, a limited of some months ago, SR Ragaraja, SSR Amaterasu, SSR Dakki). Amaterasu is very important for a good fire team.
You only have the passive bonus of your main Eidolon and the friend Eidolon. Secondary Eidolons give the attack and HP and active skills, but not the passive abilities. The maximum bonus of the Eidolons is the one of their maximum level; I'm not sure I understand you here.
Weapons are very relevant; each R, SR and SSR weapon give you skill that go up the attack and/or HP of Kamihime, but only those of the same element. Try to use a weapon grit with as many weapons of the team element as you can, and level the weapons skill using R weapons.
Abilities that do damage over time are very good at the beginning of the game, but lose much punch as you acquire more power. Attack and defense down, on the other hand become more useful. Attack and defense buffs have their uses, but the debuffs are more important that buffs. Those debuffs not always stack. See here what buffs and debuffs stacks.
http://kamihime-project.wikia.com/wiki/Abilities
I find normal that at rank 40 with no elemental advantage you have some problems. You need a bit of patience. For more advice, you should post what Kamihime and Eidolons you have on your team.