oil pressure drops to zero at idle?bad battery?

[petaling]

Recent cold weather but not too cold.Recent oil +filter change ,a mix of 5-50W synthetic (1.5 litres),4 litres of Penns oil high mileage 10-30W.That is what is handy in my garage.
Now on start-up(high idling),pressure at 3.Running on highway and above 60km(40mph),pressure around 3 bar(max).
However idling,oil pressure drops to 0.2, 0.3 sometimes zero today,ie nil.
Peeping thru oil filler hole,there is oil gushing into crankcase with engine running,not dry.
No unusual noise.
my car's alarm consumes one battery per year(battery is now 11 month old),Idling voltage 13.95v.At rest witheverything off(except alarm) ,voltage across battery=12.25-12.40 volts.

Could this low oil pressure be due to
(i)bad oil pressure sender
(ii)bad battery going south.
(iii)wrong grade oil,I've sucked out 2 litres of old and put in 2 litres of 20-50W tonight just in case,Tomorrow i'll know whether thatis the culprit.
I suspect the battery cos last yr right before the engines dies with the bad battery,the oil gauge would fluctates and drop to zero then engine died.Replaced battery ,problem gone.However,now there is no fluctutation in the oil pressure,just low or zero pressure when hot.
one previous poster suggest that his VR was responsible while others says oil in crankcase means pump is good and likely culprit being oil p sender.
Any experience or opinion?
Thanks