There's an oil-pressure switch associated with the VTEC system. If oil pressure isn't high enough it won't engage VTEC. That one could be caused by wiring, or maybe your oil pressure actually is low.

Yes, your O2 sensor has a built-in heater. Could be bad, or could be a wiring problem. Check resistance between the 2 same-color (black?) wires of the sensor. It should be 15 to 40 ohms.

But I don't think either of those things will cause your idle surging. How about checking/cleaning your IAC & FIT valves.