1. Does SOH CAH TOA apply to non-right angled triangles?

No, the triangle MUST be right-angled. Non-right-angled triangles have special formulas called the sine RULE and the cosine RULE

2. If you use trigonometry to find one of the angles in a right-angled triangle, how do you find the other?

Easy, just take it away from 90o. (remember there is a right angle, 90in the triangle)

3. What is one of the most common mistakes made by people using a calculator in trigonometry problems?

They have the calculator set on RAD or GRAD instead of DEG (degrees). 
Use the button marked DRG to ensure the calculator is set on DEG.