I'd start with taking the brushroll apart, cleaning out any hair and possibly replacing the brushroll bearings; and see where that gets you. That's good to do every year or so, especially if the brushroll is difficult to spin freely by hand. That could also be the source of your burning smell.
The motor speeding up and slowing down likely wouldn't be caused by the brushroll. If you disconnect the belts and let the motor run with no load on it, does the motor still speed up and slow down? I would try that and take note. If the problem still persists then you may have a problem with the carbon brushes in the motor, either being stuck or worn down.