"Am I responsible because I didn't keep reminding maintenance to fix my stuff or are they liable for not logging it and keeping track their selves?"

If you don't tell management about realistic repairs that need to be done, they have no way of knowing these things.

Preventive maintenance MIGHT include things such as changing HVAC filters and checking the batteries in smoke alarms. But unless you notify management of repair issues they're not likely to know that something has broken.

If you're worried that you might be charged for issues that are normal wear and tear do the repair request in writing and keep a copy for yourself.

Gail