Q: Codes p0441 and p0089

Those faults are two totally separate issues. The P0441 is an evaporative emissions system fault, and the P0089 is a fuel pressure regulation fault. This generation of Audi A4 was notorious for high pressure fuel pump problems. There were multiple updates to the fuel pressure sensors for the low and high pressure systems, as well as problems with the camshaft follower that drives the high pressure fuel pump. They also had frequent problems with the in tank fuel pump, which delivers fuel to the high pressure pump. The evaporative emissions code could be as simple as a failed purge valve, which was also extremely common for these vehicles. The carbon canister starts to degrade and contaminates the purge valve, so the fix is to replace the canister and the purge valve together.

The fuel pressure faults are the most likely cause of the rough acceleration and hard starting, though both issues should be addressed to achieve proper performance. The purge valve is easy to replace, the canister is more difficult. Checking the fuel pressure system will require a capable scan tool, as well as a mechanical fuel pressure gauge and a knowledge of how the high pressure fuel system works. Working on these high pressure fuel systems is not advised unless you completely understand the operation and are very comfortable with them. I strongly suggest having a qualified professional, such as one from YourMechanic, diagnose the check engine light for you.