Caro isn't really a summoner, other than of Einharts. Fried is the only thing she ever brings, and he's with her all the time in tiny form. It's not really the same as Lu or Corona, who bring or create all sorts of different things. If Lutecia could only summon Garryu, then Caro's abilities would be comparable.

I always assumed that Einhart gets a vision of a fight or battle, remembers the technique used, and tries it out herself in her home gym. The way she described it earlier, it isn't so much that Einhart gets some snippets of memories in dreams. She's actually plagued and cursed by them. She has such vivid memories of her ancestor's lives, emotional states and all, as if she had photographic memory and lived these events herself. It's more that in split seconds, she recalls when her past self used a technique against so and so, and uses it in her present.

She's exceptionally calm in battle, like it's all stuff she's done before and going through the motions. That's why she was so surprised by the Unchain Knuckle. She used a new and novel technique for the first time ever.

Each of the three Belkan "rulers" are different. Ixpellia actually is the same person (I'm still hoping that gets animated some day), Einhart has near perfect memories, and poor Vivio is just a clone. In some ways, Vivio is the most free. Now that the Cradle is gone, she's no longer trapped by her legacy.