$2 notes usually come in $200 straps or 100 notes. sometimes they will just get a brick of them which would be 1000 notes, which will be 10 100 note straps. as far as if they are new or old it all depends on what the reserve sends the bank. its kinda a crap shoot.
Well the BEP is still making them and the Fed is still getting them from the BEP so I would think the banks could order them. It's just that most banks don't because people don't ask for them. Talk to your bank and I'm sure you can probably get them.
My bank orders them for me and usually prior to the holiday season and Chinese New Year they got them. Again, it does not hurt to ask, but I would not pay a fee.