Is it appropriate to negotiate a part time job offer?

[Miss Lovely Candi]

I have my second interview tomorrow at an non-profit university. I have my Bachelor's and the position I'm being considered for is currently part- time, with the possibility of full time employment later on. The title is Project Assistant for the Regional Educational Academy for Leadership (College of Education). I would be required to update the web page, Facebook, and Twitter. Also, design marketing materials, as well as some event planning and various office duties.
This is my first time being in such a situation and I don't know if it is appropriate to negotiate salary, hours, and other aspects of a potential job offer. Is it? And what do you think a fair salary would be for a recent college grad with some experience in design and marketing?