Answer
a. Yes.
b. Yes.
Work Step by Step
See the diagram.
If the two charges have opposite sign, then at the point marked A the electric field could be zero. On the line to the left of Q, the electric fields from the two charges point in opposite directions and could cancel. Because point A is closer to the smaller charge, the field that Q creates there could have the same magnitude as the field created by the larger charge.
If the two charges have the same sign, then at the point marked B the electric field could be zero. On the line between the charges, the electric fields from the two charges point in opposite directions and could cancel. Because point B is closer to the smaller charge, the field that Q creates there could have the same magnitude as the field created by the larger charge.