What is part of the "submission package"?

It varies. Generally, in my understanding, it's the agent-written query letter and the ms. There may be a synopsis. Again, though, this is just my loose idea of it. Certainly you should ask your agent if you're curious.

And yes, agents submit simultaneously, and you want them to! That way you have the possibility of multiple offers and auctions. I wouldn't trust an agent who didn't do simultaneous submissions, frankly.

I think it's more or less a generic term, and that the exact "package" varies with the type of work being submitted. Probably a cover letter from the agent, your full manuscript or sample chapters, chapter outline, could include a synopsis--if you sent her one, more than likely a proposal if it's a work of nonfiction, and author bio. I don't think you should be embarrassed to ask your agent what will be included, and a list of the publishers to whom she intends to send it--and editor replies as she receives them.