For 1) I found that an equilibrium exists for Wage = 1/2

For 2) I found that workers with Theta >= 1/2 will submit to the test

For 3) I am unsure how to do part a)

I am unsure of my answers for (1) and (2) and stuck on (3). I'd appreciate guidance on all three, but if you can only do one question, then I'd prioritize question 3. Thank you so much!