Two - How could one measure the thread to thread distance accurately to
see
how much error was created when reindexing after moving? Looks like
thread
micrometers only measure the diameter.


Make a rig with two nuts, possibly (probably?) each made with some way of
getting rid of play/backlash. Fix them so they don't rotate but allow some
motion along the length of the screw. Start with them both on one side of
your "join", measure the distance between (marks on) them, then move them so
one is past the join and measure again.