Am I responsible for smoke damage if my apartment didn't come with smoke detectors?

Yes, you bet your life you're going to be held responsible. Your negligence, your responsibility. Besides that, not that it matters, smoke detectors wouldn't have prevented the fire or the smoke damage anyway. Nope, that was all your doing, so it's all on you. If it really was a short in the battery, then it will be up to you to sue the drill maker for any financial loss that you will be required to cover. Your landlord will cover his losses from you. And, if you can, you will try to cover your losses from the drill maker.

The only difference a lack of smoke detectors might have made is, if you hadn't installed them yourself, if the apartment had burned up and you became injured or died or suffered a loss of property because no one was alerted to the fire, which smoke detectors would have otherwise done. In that instance, the landlord would be responsible to you -- or if you had died, your next of kin -- for the loss. Otherwise, the smoke detectors, whether they were there or not, whether you put them in or the landlord put them in, are completely immaterial. Your having put smoke detectors in instead of your landlord does not mitigate your responsibility for the fire or the damage it caused.

Rechargeable Lithium batteries self igniting has been a major issue from day one...even downed the fleet of Boeing 787 aircraft after a battery fire, until they engineered a cooling system to lessen the possibility. Automobiles with lithium ion batteries have gauges that read 100% charge at 80% and chargers that stop at 80% charge...millions have been recalled in the USA ...

Your issue would be with the company(s) that manufactured, marketed and sold the drill,also file a complaint with the consumer protection office in your jurisdiction.

Stanford University claims to have designed. a lithium based battery that won't catch fire...but that'll be years before production...Smart move storing them on the nonflammable stove top,you likely averted another house fire. Any type battery has a risk of fire.

YOU are responsible for the smoke. It doesn't matter if there were smoke detectors, which wouldn't prevent smoke damage in any case.

Note: Unless the stove was on, and THAT caused the fire, there is NO WAY the drill battery could cause the flashlights to ignite.

Whether there is smoke detectors or not YOU caused the issue so YOU are responsibile. You should have never left a drill and flashlights on a stove. Plus smoke detectors would have notified you of it possibly earlier they would not have stopped it from happening anyway.

For legal questions ask a local attorney.