1. Airplay is not supported from the Tivo App, for in home or OOH streaming.
2. Not familiar with apps on the Mac but there is an equivalent to the Tivo Desktop software for the PC. It allows transferring shows from the Roamio and back. It does not allow the streaming that the iOS app has.
Roamio Pro (6TB)
Roamio Plus (3TB)
THD 2TB x 2 (retired)
Humax S2 300GB (retired)