1. I believe it would need a non-volatile controller chip, to disable access to the RAM while the system power transitions between on and off. The MMC mappers probably do something similar. There's also NV-SRAM chips available that have the controller + battery all in the same chip, those should work.
2. I'm not sure. I'm used to holding the reset button down, having little interest in losing my saves I usually did that with any game that used a battery. If it's unneccessary in MMC3 games, I'd guess it's a bug in the MMC1.
3. Have you tried that yourself? I know I've lost my save on Genghis Khan quite a few times (which uses MMC1) on a top-loader, but I'm not sure if that was related to the reset button or a bad contact. It worked fine after I was more careful with it (saved for few years now, and still unfinished, heheh).
Hopefully someone else knows more about this than I do. It'd be interesting to understand what the deal is with that.. and if any NVRAM controllers (like the ones made by Texas Instruments) can handle that problem.