Answers to your questions in order:
1. Yes - that's what I used to do with my CA-14s > battery box > M10 when recording quiet choral music. Although I can't attest to the quality of the mic in on your recorders, that got me a decent amount of extra gain on my M10.
2. Definitely yes. More voltage = mics performing closer to spec, and insurance in case things would get loud. You can still go mic in but PIP set to Off.
3. Probably not. It's likely that your're going to get more of the recorder's self-noise that way. Even when I was using my M10 as described above, I always was on low sensitivity, and boosted in post if necessary. Much better results than the other way.
4. See if you can get there during rehearsal / sound check and set levels to peak no higher than -16. That leaves you a good amount of insurance in case things get louder, and you can still boos in post like I said.