Jumping RPM on speedometer

If those are the only items that change I would suspect a failing speed sensor, or damaged wiring to it. The speed sensor works with both of those systems.
Because the ABS lights come on there should be a code stored in the ABS controller. A scan with a good scan tool should show what the problem is. Do not bother with the free scans most parts places do, they only scan the engine computer, not the ABS system.