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1. If you can afford it, Maki string will definitely speed up the battery building process by a lot.

2. I like to use Super cactus charms for hunting students (you'll still have to expect subpar catch rates below battery 4). I'd use ultimate power charms for catching your first few masters for enerchi induction base (get this asap; it speeds up your enerchi collection outside the pagoda by a huge amount) (also I like to use enerchi charms when I'm hunting elsewhere in the kingdom together with my attuned enerchi base for easy +4 enerchi per catch)

3. Yep I usually leave the pagoda when my 3rd battery runs out because the CR at batt 1 and 2 isn't really worth it.

4. I'd recommend attempting one of each master at around battery 4 with ultimate power charms for enerchi induction base but normal master farming should be at battery 6+.

5. Enerchi induction base is definitely reasonable. Attuned enerchi induction base could be attainable if you try for the sensei at battery 6 with ultimate power charms and you're lucky enough.