I've hired a part time person who will work
Tue, Wed and Thu 1-5pm
And
Saturday 6 hours.

What are the laws (if any) about breaks per hour?

I want to be fair. Back when I was working hourly, we got some break periods on occasion, but I don't remember the details...

What is the law about part time workers and their break periods?

Not sure about breaks, but dinner(or lunch) must be taken on any shift over six hours.