leopoldr, welcome to the forum.

BIAB can do everything you are asking. I play solo with my backgrounds weekly. I use my MackBook in live performance using the built-in sounds therefore not needing any modules.
All the mixing is done in BIAB and I plug into one of 4 available PA systems for sound reinforcement and for vocals. In hundreds of jobs I have NEVER been questioned about the quality of the instruments from the Mac or the RealTracks and I am playing where the entire audience is focused on the music. I mention this because you say you are going to be doing background music.
To anyone who is using a Mac I strongly recommend Boom2 which is a download which allows you to control the EQ of the MacBook. As I mentioned I have 4 choices for sound reinforcement and the Boom2 lets me have different EQ settings for each.
Personally I would not use an iPad for live playing. I don't think you have enough control of the music. I keep a backup of all my BIAB songs on my iPhone and have used the phone to perform with several times and it is much more difficult for me. As Bob"Notes"Norton indicated it takes too much time between songs.