1. Yes.
2. I asked that very same question in a letter to John Gambling (Rambling with Gambling radio show) in 1967 when I was 13. I heard him read the question on the radio, but never got the answer. Until the movie Bull Durham came out. The term originated in Durham, NC. The area where pitchers warmed up was under a sign for local tobacco company Bull Durham, which of course featured a large bull. The area became known as a "bull pen".