Im not exactly sure, but my 310 would last 3-4 months.
But I never turn it off either, always forget. So you may be able to get a bit longer from it.
It takes 1 AA battery.
It does fine for gaming. Just a basic 3 button mouse with nothing fancy.
Theres better out there that are more configurable, more buttons etc, but those are also getting into the pricey gaming mice.
For a basic mouse, at a reasonable price, I can't really find anything to complain about with it TBH.