2. Alto sax is always in the key of E flat. That means the note called A flat played by an alto sax would be C on the piano. Likewise tenor is always in the key of B flat. A huge advantage to this arrangement is that the fingering is the same no matter which instrument you are playing; that means it is up to the composer to transpose notes as appropriate. The saxophone family is amazingly cohesive and consistent because Adolphe Sax invented it in one fell swoop.
3. Well-trained classical musicians can transpose at will. I read a story by the composer/pianist Andre Previn whose touring orchestra was late to a concert hall due to the bus driver getting lost. He was playing the piano in a concerto. What he didn’t know was that the entire piano had detuned up half a step. It meant that The moment he sat down to play a concerto in C minor he was therefore playing in C sharp minor. The orchestra caught this immediately and everyone transposed up for the rest of the concert – on the fly.
Edit: I mysteriously screwed up keys of alto and tenor sax, both of which I play. Idiocy caught by klez and duly corrected.