I just have a couple of questions concerning electric field.

Perhaps someone could just tell me whether or not I have a grasp on this conceptually?

Is the electric field in the direction of path zero at every point from a to b in a straight line?

I would suggest that if you were to make a line segment from a to b, the only position along that line where the electric field would be zero, is in the middle where the line is perpendicular to the line of force.

What about along the equipotential line joining a-b?

The electric field would be zero along this line..

Is the electric field in the direction perpendicular to the path zero in the straight line joining a-b?

I would say no. It is never zero along this line.

What about the equipotential line joining a-b?

Definitely never zero.

Thanks in advance!