I check my gear about three times per year, sometimes four. Checking gear means going through every item in every FAK to replace anything that's expired (replacing expended items happens almost immediately), checking every device and every battery, checking every tool and servicing any that need it. The rechargeable battery in the weaponlight on my shotgun gets charged as well.

Every month I recharge the jumpstarters kept in each car and charge my wife and daughter's low-end HTs. My high-end HT has a very low self-discharge rate and doesn't need charging as often; I do that with the gear check. My super-cheap-I-won't-cry-if-it-gets-stolen-from-my-car HT also, weirdly enough, has a very low self-discharge rate. Other rechargeable devices are recharged as they are used.

Water kept in the vehicles gets replaced as it is used -- when I hit half a case of bottled water I put in a full case.

Temperature extremes can definitely have an impact on an alkaline battery leaking. It seems unlikely to me that the flashlight had a significant impact on that -- back when I kept alkalines in the car this would happen to them in the cardboard package.