In my experience the answer is no, no standard forms. But I've been working under the radar of Status Quo so I'm sure there is something out there.
I think you're more likely to sign an agreement (often a NDA - non disclosure agreement) but again that's something the employer will have you sign, not the other way around.
My only advice is to get terms of payment really clear and in writing. It's such an unnecessarily knotted up feeling of helplessness when you've completed a gig and haven't been paid (yet), and don't know when.
As for terms and advances extending credit ... do a search on this forum. As for rate, don't ask, search. :)
I'm sure someone will pipe in with more knowledge than me on this subject.