To ensure that I do not miss anything, I will go point by point with your questions. You asked:
Does she have to go through any court process to notify me as I would be served papers or proof of her asking me to vacate or can she just write it down and hand it to me or mail it to me?
Proper notice requires that you be served in person, or the notice is affixed to your door, or you receive it by mail.
Does she need to go through a formal eviction process?
Once those 30 days are up and you are still on premises, yes.
I would like to know how long or what date I would have to vacate premises.
You would need to vacate by end of that notice if you wish to avoid an eviction.
I need time to find somewhere to go. She can't shut off utilities even if she pays them, electric or water?
That is correct, she cannot.