a 2011 jetta. brake pedal is hard no pumping action. the car show chekc engine. the idle is not smooth.
That CEL (check engine light) is just a kid in class waving her hand trying to get you attention because she has the answer. You need to have the codes read. Some places will read them for FREE. Try Autozone or Advanced Auto Parts. Get the exact code (like P0123) not just their translation into English and post it back here.
Get the fault codes downloaded.
Also, try a “quick trick”: try disconnecting the vacuum hose to the brake booster and clamping it off. If the rough idle disappears, the problem is a booster with a vacuum leak. Fix that, reset the ECU, and you’ll be good to go.