Question

when work done is minimum

Answer 1

 Since work depends on the cosine angle between the force and the displacement, minimum work will be done when the cosine of that angle is zero, or the angle is 90°.  Yes, good point, negative work would be less than zero work. I have to admit I was thinking about the magnitude of the work. (Despite what Ajmal Mureed says, work is a signed scalar, and does not have a direction.)