1. I am so stressed out.

2. I am so stressed.
(What is the differrence between them? Does 'out' mean 'completely'?)

3. But Nikki has a childlike innocence.
4. But Nikki has a childish innocence.
(#3 is right, but how about #4?)

5. I didn't think you were so childish.
6. I didn't think you were so childlike.
( Are both OK? Is the meaning different between them?)

(Is 'childlike' used only positively? Is 'childish' used only negatively?)

The answers to your last two questions are yes and yes -- generally.

Knowing that, how will you answer your questions for 3 - 6?

1 and 2 mean the same thing.