Unless you use a mono-spaced font I would say it's impossible to set the first since there are a lot of narrow characters in a proportional font, but the second you can do by setting the leading. There are 72 points per inch, so you would need at least 12 pt leading. Characters per inch would vary with the size of the type.
I am planning on using 11 point Arial font (which isn't mono-spaced). My line length is 8 inches (576 pt - so I guess I can't exceed 8x15 = 120 Characters in a 576 pt line). I found this blog on setting characters per line (How to Tune Typography Based on Characters Per Line) but I'm not sure how to apply that within InDesign. I agree that to do this with any accuracy would be impossible, but I guess I would somehow need to adjust the hyphenation and justification settings so that the maximum does not exceed 120 CPL.
but I guess I would somehow need to adjust the hyphenation and justification settings so that the maximum does not exceed 120 CPL.
There's no setting that allows you to set the lines' character counts. You could get the average CPL via a script, which would make it easier to set the text frame width to get a target average.
This AppleScript (OSX only) displays the average for the selected text:
tell application "Adobe InDesign CC 2014"
set ls to count of every line of selection
set cc to count of every character of selection
set a to cc / ls as integer
display dialog ("Average character count per line of selected text is: " & a) buttons "OK"
display dialog ("Please select some text") buttons "OK"