I think you bring up some interesting questions, but I'll only be responding to the quoted part above.

Searching for "Collatz conjecture" on Google Scholar revealed the article The 3x+ 1 problem and its generalizations by JC Lagarias (1985), among others. (You will need JSTOR access to see that full article from the link.)

Also, a quick search on regular Google gave a site you might be interested in, Collatz Conjecture Calculation Center.

I'd like to use these questions as programming exercises, but I have limited time. I'll let you know if I come up with anything that could be useful.