Testing new programs: Can you cite source(s) that quote what the
average number of times a new program is compiled (before moving it
into Production)?  I was told once it is about seven.  When a software
developer writes a new program, it takes several tries to get to work
at all and more to ensure proper flow of logic as well as integrity of
error routines.

I don't think you can attempt a decent answer at this without stating
the kind of program - and probably something about the programmer
population in mind (such as perhaps students on small homework
problems).

In work of any size partial programs will usually be compiled and
tested many times before the program is complete.  Some places build
their software daily so the number of compiles will be related to the
age.