I would say no...if the recipe calls for all purpose, then it's best to just use all purpose. That might ruin your cookies... 
You cannot interchange self-rising with other flours; it has baking powder in it
If you want to decorate your cookies I would say no. the cookies will spread and rise.
I don't know; if you had time to experiement, I would say try it; if you are in a crunch, I wouldn't risk it.
What the heck.... I could always try it and if it didn't work I could go out and get some AP flour!
Why bother wasting time and ingredients? Baking is NOT like cooking where you can substitute ingredients at will without much of a change to the end product. Unless you know what you are doing it's recommended that you stick to the recipe as close as close as possible. You could end up with cookies that are a different texture than what they really should be.
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