Fafnir buffs the attack and defense of your party when summoned, in addition to it's fire attack. Passively, it boosts the power of your party's fire and water attacks if it's set as your primary/support Eidolon.
Generally speaking, keep Brynhildr if you get her; you won't regret what she brings to your potential party compositions. She covers a lot of bases, and does it very well.
It works almost exactly like Granblue Fantasy, the whole game does really, but your 'classes' are always female personifications of various legends(Arthur, Solomon, Hercules, Gilgamesh, etc. - and yes, you get to screw their brains out after leveling them) and you don't get to see the actual weapon you equip in combat. There are Tiers and support/EX skills you can carry between classes and all that jazz.
Probably the biggest adjustments coming from GBF to KamiPro is the lack of ability to queue up multiple skills at once in combat(you do get an auto-combat feature though) and support summons only being instantly available if they belong to your friends(if it belongs to a stranger, you have to wait the charge up time - like your personal summons). The Union/Crew system is a little different as well.. with elemental guardian deities instead of airships - I don't think there are co-op missions, but there are events centered around doing stuff together with your Union.