I was iroining several different pieces of white-on-white last night. All but two came out nice and crisp with no wrinkles at all. Two have wrinkles everywhere. ALL of the pieces were starched at the same time, folded, and all went into the same zip-lock bag and into the fridge for an hour before pressing. All had previously been pre-washed.
I noticed that the two that are still wrinkled are not as tight a weave as the others that are crisp. So with this I'm chalking it up to quality of fabric (even though all were purchased at an LQS).
Now ... if I was using these whites in an area on the quilt that was going to be large enough to show wrinkles I would be concerned that it would ALWAYS look wrinkled. However, none of them will be larger than 1/2" square when finished so I'm not worried and will use them as is.
So I think the answer to question 1 and 2 is that it probably has more to do with the quality of the fabric. When I purchased the two suspect fabrics, they were not wrinkled on the bolt. The wrinkling did not happen until after I laundered them.
Can't help you with question 3.