What is the "required" amount when using Plumber's Putty
You only need a enough to cover the ring area and keep the flange from leaking.  It really depends on the depth of the offset space and how your flange fits into it.  

I think normally I would probably lay down 1/8 inch.  However I have ran across some new modern bathroom sinks where I used 1/4 inch because the ring was deep.


Yes.  It sounds like your application was the perfect amount.  You really should have a slight amount come out on tighten.  If you don't then you don't know if you have enough.  If a lot comes out then you run the chance of not being able to tighten enough and getting dribble leaks.  If you have too little and there are no leaks then you will still have a "crack" around the flange where water pools.  Might never leak but isn't attractive.
You have to tighten the ring to test for leaks.  Once the ring is tighten it is permanent.  If you untighten the ring then you could cause the putty to move and introduce a leak.  Often if you untighten you have to reputty.


Also I want to note two small things.  #1 - Do not use rubber/plastic gaskets instead of plumber's putty.  These are now included in a lot of kits.  First sometimes they fail right away.  Second the material can break down and it can fail in near future.  Plumber's putty isn't perfect but it is much much more reliable (also don't mix plumber's putty with these gaskets).  #2 When you apply your plumber's putty you want a little squeezing out - you should get a little squeezing out all around the circle.  If you get a lot on one side and none on the other I would start over.  The amounts squeezed out don't have to be perfectly symmetrical but you don't want to see none in an area.