They are technically rechargeable. Not very often and their capacity deteriorates quickly, but there are specialized alkaline chargers that allow you to recharge them a couple of times.
You can tell whether they’re full or empty if you drop them on a hard surface. Empty ones will bounce slightly and make a “brrrt” sound, while full ones will stop immediately and make more of a “tock” sound.
Some fun facts about alkaline batteries:
Don’t think it’s a good idea to apply blunt force to a battery, but neat
You’re only supposed to drop it from an inch or so. Just enough so you can tell whether it bounces or not.
Alkaline batteries are pretty staple. You can throw them against the wall and nothing will happen.