Question

1. Ideally, the current through the rotor of a DC engine changes sign every half rotation. Is it still possible to get consistent rotation if the current spends a little more time with one sign than the other?

Answer 1

No. If you want the rotor to interact for more time, the current through the coil would be less and hence eventhough there would be a consistent movement, the speed would reduce. And there is no polarity effect, so the rotation would be same for positive as well as negative.

P.S: You could aslo tell yes to this on the basis that the time of ineraction is so less may be in the order of microseconds, that increasing it by some tiny amount. It wouldn't make any noticible changes and a smooth.