No to the last three, and probably not to the first.  If the engine spins
over, your starter isn't your problem.  When trying to re-start, push the
accelerator pedal down a bit (maybe 1/16" or so - barely press on it), and
see if it starts easier.  By doing this, you're cracking the throttle plates
open a bit, giving the engine more air (what the IAC should be doing
automatically).  If that makes the starts easier, you've pretty well
narrowed your problem down...