John,

Welcome to the forum.

If you purchase BIAB, you'll automatically get the latest version of Realband at no extra charge. They come together as a partnership.

Both BIAB and RB (Windows versions) will print lead sheet notation. I've found this quite ok for most purposes. If I need anything more elaborate, I use MuseScore. MuseScore is a freeware notation program that reads in BIAB files, too.

You other questions ...
Quote:

Can I specify an unlimited number of repeats of the song


Yep. You could set the song in "loop" mode and so it would keep (re)playing a specified range of bars. This could be the whole song.
Quote:

... if I want also decide to have only 4 repeats of the song.


That's also possible. It's specified as "number of choruses" since from a BIAB/RB perspective, one chorus means "once through the entire song". (This is the classical definition of chorus and not the popular music definition.)
Quote:

Am I correct in assuming I can do a count in of one or two bars as the user specifies


Yes. This is given by a side-stick beat (not a voiced count). It can also be show visually, which I find quite useful.
Quote:

Can I record a few solos and play back only one of them at a time to look for segements that I might want to use for writing songs


Realband will let you do this quite comfortably once you get the hang of it.
Quote:

Related to the "Primary Use" I may want to go back and rerecord (change) my rhythm track.
Related to the "Primary Use" I may want to also record the melody and the solos.


Again, this is where Realband excels.

Hope this helps,
Noel