2011 Volkswagen Tiguan engine problems

This car does not feel safe. Several times the car has just stopped. Stopped at a traffic light and started to go and car just died. No lights, no warning. I start up the car, move forward and get ready to pull out into traffic and car just dies. VW said they need to have warning lights or something so they can get the information from the computer and since there are none, it won't tell them anything. Even in high-speed driving it sometimes feels like there is a lull or that fuel is not be injected.

I was turning left off of a hwy. I attempting to accelerate to 40 miles and the car hesitated like it was switching gears, decreased in speed and started shaking. I pulled over, checked the gas cap, - it was closed. Turn car off for a few minutes, restarted, car still shaking. I drove the car to safe place off the road. The car would not accelerate past 20 miles hours. I put the hazard lights on, but they kept going off. Then I called the tow truck.