I've found some really pretty designs on the generator and I was wondering if those are up for anybody to use. I was thinking of starting a project at some point to make a pet from a design, do I need to contact the person first to make sure it is alright, or are all the designs open for anyone to use?

It is highly recommended that you contact the creator of any public designs in the generator before doing anything with them. Some people design just to design and are happy to let you use their designs, or sell them to you. Others make their designs public to garner interest for when they produce those designs and sell them. Taking these designs without permission and using them is usually viewed as design theft and is severely looked down upon.