I'm by no means an expert, but I'll see if I can help you out.
Answer to your first question: You're not really close to getting reincarnation unlocked, in my first playthrough arriving at the Moriya shrine was about halfway between starting and getting reincarnation... Assuming that you are playing the base game... And your mileage may vary (I didn't get lost in either the Hell of Blazing Fires or the Hakurei Mountain Cave, but some people I know have struggled with those two areas, but I did struggle in the Scarlet Devil Mansion, which extended my early game). But don't be put off using puppets that you want to use just because they don't have optimal stats. It's not a terribly difficult game and I've beaten it using most of the puppets in one way or another...
Unwanted answer to first question: It's not really much of a "spoiler", there's no storyline event for it or anything. Spoiler
Yes, it's in the postgame. After the credits go to the Scarlet Devil Mansion and talk to Patchouli. There should be a Patchy doll on the table north of her position in the library.
Answer to the second question: I stopped playing Pokemon a long time ago, so I'm not sure... Wisdom Eye ignores all stat changes except for Speed. I'm not sure if Unaware takes speed changes into account. If speed is also ignored in Pokemon then I guess the answer is "mostly"... Otherwise, yes, they behave identically.
Answer to the third Question: No. If your puppet has the Wasteful ability it won't use the charm... unless you change it's ability outside of battle. If your foe has the Overwhelm ability your puppet can't use the charm until the enemy puppet is either defeated or withdrawn, at which point the charm will be used at the beginning of your next turn (I think...). To my knowledge those are the only exceptions, and any other situation if it has the charm it will use it (Use limit is once per battle without the Resourcefulness move or the Economist ability).