Sorry I didn't get back sooner on your Reaper question.
When you say BIAB files, I am assuming you mean the BIAB song files. No, they will only play in BIAB ... and possibly PowerTracks or RealBand. That I don't know.
But in essence, each BIAB song file, as best I understand, is some type of proprietary midi file, which can be easily converted/ exported to a standard midi file that can be used in any DAW. So, after you make your BIAB arrangement/ song, you then take the midi file to your DAW of choice for more sophisticated midi and audio programming. Reaper, Sonar, Cubase, ProTools, Traktion, Logic, etc., all do these things ... although as I said, Reaper is in a class by itself as far as the opportunity to fully use an uncrippled, untimelimited demo, its incredibly low price and its active user group.
You've got some great advice here and since it sounds as though you already have some versioni of Cakewalk Music Creator, you may as well start there. If you outgrow it, then you can look further into the DAW suggestions here.
Good luck!
Prado