02 values do fluctuate a lot. It's not normal to sit at 0mv for awhile in a closed loop chip, but hitting that low of value in the regular up/down cycle of the 02 sensor can happen.
Stumbles are usually lean fueling, and the 02 values are reading that as well. The 02 readings are usually more of an symptom, if you follow.
Send me a run, i'll take a look.