2004 A4 1.4 Quattro. Odometer has around 130k miles, but the engine was replaced last year and has about 15k miles on it now.

Problems -
Pulled a PO411 code (secondary air pump incorrect flow) this past week. Furthermore, it started stuttering while idle and my foot is on the brake. Noticed this while waiting at a stoplight. The RPMs start twitching around and I can feel the car shaking until I hit the gas. In addition (it never ends! ), I'll turn the ignition and the car will start but turn off right away and the battery light comes on. Sometimes, it'll take 2 or 3 starts for it to stay running. A couple months ago, the car threw a code for a brake booster vacuum system error. The shop reconnected some loose hose and cleared the code, which hasn't come back. I want to say that they are all somehow related?

Would appreciate any insight on this!