1) Yes, the customers' table is the same for all the shops, it means that any account is the smae between the two. However, the basket is also shared, it means that you can actually buy products from the two shops in the same order. It can be quite handy for some shops but maybe not for others.
2) Here again, it is technically possible, but it would make some problems with the common cart. Somebody could add to cart on one shop and then pay on a different shop. I guess that this could be solved by changing the table of the session to a different one so the cart of customers won't be common between shops, but this is something I have never tried yet, so it is not guarantee to work. Appart from that, it is technically possible to have different payment module for the different shop.
A good solution of this problem would be to have different shipping in function of the categories of the products. In this way, the shipping would be equitable no matter on which shop it has been payed.
3) sams for that, it could be done by checking that alll the products of a cart are from the "free shipping categories". Then you can facturate free shipping for the cart... The problem would come when you say that the same products would be either free shipping and charged for shipping on two different sites. I is possible but look a bit strange to me...
Bookmarks