Nice question, O2 in anaerobic chamber increase the respiration process of the biofilter which is an flora which requires O2 for its respiration process. It requires minimum amount of O2.
I think, the anaerobic wastewater treatment itself should happen in the absence of DO. If DO is present, we can't call it anaerobic Process. So if DO is present your anaerobic process, it will hamper and will not end with methane production and successful water treatment.
There is no need or O2 during anaerobic process but during the initiation of microbial growth you have to provide some O2 for their respiration process, not during operation phase. i did not know exactly how to measure the production capacity,
DO should be zero and In case of quantification of methane production, you have to collect biogas produced in the anaerobic bioreactor, quantify the biogas quantity in volume (manufacture small gas lifted dome or downward directed filled measuring cylinder), then do sampling of biogas and check for methane % in GC-FID (or onsite methane quantification equipments also available). By using quantity of biogas produced in given time and percentage of methane, you can calculate Methane production in respective time.