This is my personal experience only
Most places that have personal days, say they “prefer” if you schedule them in advance. Unless it's written in the manual, that it must be scheduled, it doesn't have to be.
If you have a no fault attendance policy , you don't have to say why you wont be there. Unless you are actually sick and have a Dr note.
You do not have to sign a write up, if you don't agree with it. Signing it means you agree with it
If your workplace has a strict late policy, where 1 min late is an occurrence/ point :
When / if you are late, make it with it. ( If you can afford too)
Don't rush and be 30 min late. Be a few hrs late, because 1 min has the same point value as being 3 hrs late.