Correct.

Yes, an index mark on the tap and a light tap or two to set the tap so it bites straight away upon rotation should get the job done. May take a couple of attempts.

I found a club member with a 4" or 5" benchtop lathe. I'm sure it's good enough for this type of light work. I'd have one myself but need one so infrequently I can't justify the cost. I suppose if I had one I could create projects but have little interest in metal working. I do enjoy woodworking however and have a nice cabinet shop.