Metal ruler and pickups

For years I've always used a metal ruler to measure pickup height, one of the small ones in 32nds and 64ths, never had a problem.

 

No. Extreme heat would however. Do not get a soldering iron too close.
A simple way to set the distance between pick-up and strings is with a set of Allen wrenches. Just get a 3mm one to run between both while fretting a string at the end of the neck and you'll have your "recommended nominal height", from which you can deviate as much as you like.
Or stack a few guitar picks of known thickness to the same effect. I used to measure string action this way.