1. How far apart must two protons be if the electrical force of repulsion acting on either one is equal to its weight?

Answer 1

Are you referring to the proton's weight in the Earth's gravitational field, or the electrostatic attraction force to the other proton?

I have to assume that you mean "weight in the Earth's gravitational field", since the gravitational attraction is less than the electrostatic repulsion at all distances.

So, set
M*g = k*e^2/R^2 and solve for R.
M is the proton mass
k is the coulomb constant.
e is the proton charge
g is 9.8 m/s^2