My tire was slashed. Replaced the inner tube, but should I replace the tire as well?

A corollary point - you need to find a way to protect your bike from damage while it is parked. Overnight is many hours of time when your bike is exposed and there are few people around.

If you were in a rack, park it further away from where people walk.

If your bike was blocking someone else, don't.

If you had unwittingly taken "someone's spot" then simply use another parking slot.

Can you store your bike overnight inside, in a garage or lockup, or somewhere else more-secure ?

You already know the answer to this question.

Slashes in the sidewall tend to open up as the pressure from inner tube is pushing the tire further apart. If you're lucky you might escape with a simple pinch flat. More serious problems include:

• the inner tube pushing through the sidewall rubbing on the frame or fork causing the inner tube to burst like a balloon.
• the inner tube removing the bead of the tire

Either of these I wouldn't want to happen at speed.