I am a home owner and I am renting out a room in my house to a family. I have served them with a 3 day pay or quit and than a 30 day notice. They refuse to pay rent for the amount of time they will still be here, so my question is, do they still have to pay for the amount of time they are here from the day of the notice?

Yes they still have to pay and you may sue them for it if they don't

I have the same situation. If I sue them, how do I go about self-filing it with the court? Is it with the same forms of summons and complaint forms or is it with another form?