What are the fuctions of oxygen sensors on the 1997 pajer V6 3500

have the fault codes read
as the engine light also reports on transmission problems as well as the engine
changing oxygen sensors (O2) will not fix the problem as there is an heated oxygen sensor (HO2S) in the exhaust manifold that controls the air/fuel ration settings and that is affected by a vacuum /exhaust leak

Check for any cracked vacuum hose, Throttle clean it Check if you have any place sucking air.

Hey, The o2 sensor affects the fine tuning of the engine. it is used to tell how well the engine is burning off the fuel in the combustion process. if there is too much oxygen, then it will adjust the air/fuel mixture accordingly and vice versa. If the car runs too lean or to rich you will loose power and possibly damage your engine. It would be a good idea to replace if its faulty.

Generally no.
Oxygen sensors usually work or they dont .
If it was worn out usually you would see a change in fuel consumption.
It most probably is something being affected by the heat such as a cracked head which the crack will open up as engine gets hot.
It could also be from spark plugs and or leads breaking down, as overtime they are affected by heat.
other things affected by heat a electrical wires and connections,
Hope this was helpfull

Replace all spark plug first.
It Cheap and ez before replace oxygen sensors

the check engine light also means there is a sensor telling the engine something needs fixiing :ie Repace oxygen sensor or something of this nature that does not affect the over all performance of the vehicle, maybe less to the gallon but thats about it.

No the oxygen sensor is located in the exhaust manifold up stream from the converter lessening the back pressure will only make more movement of air and a cleaner burn from your engine to the sensor

you don't want to take the cat out because the oxygen sensor will make the check engine light to come on.
the up stream oxygen sensor is called air/ fuel ratio sensor, with out that one your engine will not run right

Look before and after the catalytic converters. They will have wiring connected to them.

change the pcv valve its under the intake manifold