SSR book? I'm assuming you're talking about the grimoires. They are used for break limiting SR and SSR himes. The only SSR weapon is the Ixid Blade.
You'll want to use weapons with the same element as your himes or they won't get the skill bonuses, so using a thunder weapon with a wind hime is still doable but you won't get the additional damage from the skill bonus as they're not thunder himes. So you want to keep all your weapons the same element as your current hime party.
Eidolon on the other hand, you only need your main to have a passive to match your team, the sub eidolon can be whatever you want.