The car in question is an MK4 - GLS model with a.

The car in question is an MK4 - GLS model with a 2.0L gasoline engine. On very cold days after sitting for approximately 3-4 hours the cars starts fine but in a few minutes the motor dies off. If restarted immediately it works fine and drives OK until the next cold start. I also noticed when driving it sometimes jerks as though the motor wants to stop, but catches on, Almost like its is getting starved of gas. What I have checked - Fuel pressure & filter, Battery and alternator. These check out fine. It does not show any Check Engine Light, but I scanned it just the same and pulled these errors :

4 Faults Found:
16795 - Secondary Air Injection System: Incorrect Flow Detected
P0411 - 35-10 - - - Intermittent
16518 - Oxygen (Lambda) Sensor B1 S1: No Activity
P0134 - 35-10 - - - Intermittent
16524 - Oxygen (Lambda) Sensor B1 S2: No Activity
P0140 - 35-10 - - - Intermittent
16517 - Oxygen (Lambda) Sensor B1 S1: Response too Slow
P0133 - 35-10 - - - Intermittent

My question is whether the replacement of the oxygen sensors may help alleviate this problem. It looks like the have never been replaced before. Can they be the cause of these symptoms? Also I am aware the secondary air injection system has a problem. The secondary air system has had a problem for the past 3 years but I have not had these symptoms arise. The oxygen sensor errors appeared at the time the car started having these problems.

Any help in regard to this matter will be highly appreciated.

Thanks

Eric