Your tiles, including upcoming tiles, refill at the start of your turn if you still have health, and then effects like ! tiles falling off happen during your turn.
To activate equipment that require manual activation you click/press thier icon.
There are plans to release the OST when my brother is happy with it, although he's currently sitting on a big music rework that should be coming soon™.
For most enemies where defeating them counts as murder, you can make them run away by hurting them enough (enough usually being less than half health). Enemies that count as murder that wont run away only happen if you're already on a murdery path or choose a murdery event option. They'll have if they will run or not listed in their statuses with a little exit icon.