Not sure if you've found your answers already...
I do have some doubts about the why you would want this all, but in short regarding your specific questions:
There is a one-one relation for Shoppingcart and Customer, this is also connected for restoring shoppingcart when you've left the session. So out of the box no. You might be able to customize it, but you'd have to handle quite some logic.
Why would you want it to be multiple orders? Can't you just extend the tax and shipping costs calculations?
Tax is calculated on product level, but shipping costs usually are calculated apart from the products usually because those prices are not displayed in the order VAT, or can't be used with discounts or vouchers and such.
Could you describe a valid use case why you would need this. I think you could easily enrich the process with adding additional (optional) calculations to your checkout that check for properties in these "groups".