bio undergrad so take w/grain of salt
1. No, because serum does not contain any cells that have the markers of a bloodtype. You're just transferring the antibodies pretty much. When you spin down a blood sample in a centrifuge, the bottom pellet contains blood cells, the supernatant is plasma. From that supernatant, when you get rid of clotting factors, the remainder is just soluble molecules and antibodies.
2. Maybe. Serum can also contain viruses, but I assume the serum will be treated with chemicals to "clean it up" and just isolate antibodies.
No you don't plasma can be used on anyone. Which is one of the benefits, unlike whole blood it's safe to use with any blood type. Can also be stored and stockpiled.
And yes you can get HepC and other viral diseases from it.
Beyond plasma therapy plasma can be purified as well. Which makes it easy to administer. (See Gamma globulin).