Is it best to store attached to the rechargeable drill or off ?
18v. Lithium-ion battery.
Infrequent use with several weeks in between, Battery not discharged fully, <50% used at a time.
Recharge before storing? I heard that battery has a finite number of charges?

Store it about 75% charged.
store at Room temp.
remove from device.

The number of charges are not infinite, and the battery will develop a memory. They're not as sensitive as some, or as rechargeables used to be, but the battery life will become less.

I have several rechargeable drills and screw guns that I keep multiples of batteries for. I know some guys that just keep a battery in the charger. I don't, partially because I don't think it's beneficial to the battery, and partially because it's a potential fire hazard. When a battery no longer turns the drill or screw guy, I remove it and discharge it in a small flashlight that takes the batteries, before putting it on the charger.

I would suggest reading the manual for the tool in question.

I recently purchased a 56V leaf blower. Per the manual it is OK to leave battery on the charger. After an extended time on the charger the charger will discharge the battery to a storage charge 50%.

I know from my RC hobby LiPo batteries storage charge is 50% approximately 3.8V per cell.