Once rooted cuttings have been properly hardened in 1 gal. pots, should they be
treated like tomatoes, squash i.e., not moved outside until last frost date 
(June 1 in our area) or a few weeks earlier so that a light frost would not
harm them?

Hi John,
You'll have to do the "fig shuffle". Bring them in when there is a chance of frost.

I had the same question. What nighttime temp is safe for newly-rooted cuttings?

In my area I wait until the night time temps stay in the mid 40* range on a consistant basis...after that it's clear sailing for me.

Yes, its like starting any veg seedlings, it does help to get them outside and "hardened off"  but consistent nighttime temps about 45 degrees is needed not to stunt the roots or have leaves drop. I do sometimes take a large commercial kitchen size cookie tray, place a growers propagation heating pad under it, and place the 1G containers in there with some water in the tray, the water stays warm from the heating mat, and that helps on a patch of raw low 40s nights in April or May if I get too lazy to bring them in and out.  Warning ....thoughts like this spark discussions of should I get a cold frame, then a small greenhouse, then that spawns I need a larger one......