It certainly won’t auto-discharge, but like most batteries you’ll probably lose a couple of percentage points, looking at my AirData (which I’ve been doing a lot of these last two days!) I see a good few of my flights start with a 97% battery, again probably just where they’ve been standing a few days.
I’ve noticed my controller drops off a few percent too, if not used for a while. It’s not discharging, just natural loss I guess?
I’ll let someone with better lipo knowledge answer the other parts of your question 