1. Should answers to trigonometric equations be given in degrees or radians?

It does not matter. However, if you are doing a question which is in radians then your answer should be given in radians.

2. How many solutions do trigonometric equations usually have?

Unless the domain is fixed, that is the possible values between which the solutions can be taken, then there are an infinite number of solutions possible. Usually solutions between 0 and 2π or 360° are required.

3. What is the best way to deal with a trigonometric equation such as     4sin x = 1?

The easiest way is to divide both sides by 4, which gives the equation sin x = 0.25 which is easier to solve.