I have seen Pat Neshek's website, but I wonder if you are a Jeter or Pujols type name, could you have your agent call up Topps or Upper Deck and get them to pull you one each of all your cards?(1) they get stuff for GU from different places...some is direct from the teams and players, other stuff they get from auctions or private collections.
(2) it varies...when UD was in court once it came out that they payed T-Mac $50 per auto and some other players were getting $3 TO $20...i've heard Jordan gets $150 a pop from UD.
(3) no...if you read Pat Neshek's blog/website you will see he tries to track down his own cards just like any other super collector does. I know when Score did the Mantle Autos back in the 90's the Mick got set #7 as part of the deal. So sometimes they do get cards...but for the most part they don't get anything special.
also from what I understand the money from cards goes to the collective MLBPA and MLB properties rather than the players directly....they handle the negotiations and all that sort of thing and collect all the money from cards.