Battery charge level as the maker suggests - many 50% or "40-60%" during long term storage for LiIon types, or perhaps you have other tools to keep the batteries active.
I wouldn't worry about draining the bar oil, but I'd expect some dripping, so you might reduce that by attempting to drain it as much as possible. Or just put it in/on something that will catch the drips.
Sawdust cleanup couldn't hurt, but is not usually critical unless it's being stored in an area that's also damp (which is a bad choice anyway...)
Most of what sticks to the saw is somewhat oily from chain oil so not very corrosive. I tend only to clean it out when changing the chain or flipping the bar. Hasn't caused any noticable problems. Now, if they are really in "every crevice" including whatever cooling air intake, that would not be good - both the gas and corded electric saws I have were well-enough thought out to keep that clear, so I'd expect no less of a battery saw, but if it's not keeping the chips away from the air intakes, those need to be cleaned.