Yes, a tired battery can cause communication errors between the modules, leading to false codes. Check all connections...not sure about the fuse, but I'd check the fuse box in the engine bay (high amp-Fan/DME).
That code usually indicates that the DME has lost control of the fan, causing it to run by default, to prevent overheating. Do you have a rodent problem? Check the wiring harness on the fan shroud for damage. How old is your battery? Could be a loose ground or blown fuse as well.
Had my pump replaced under warranty earlier this year...same symptoms as you, low coolant notice, could see the dried fluid around the pump area, not unlike your photo.
Do a title search for "hesitation "...few threads on the subject. From there, you can determine if you think it's worth updating the software. I was experiencing hesitation from a stop and got an update...hasn't happened since.
Have you tried disabling the start/stop function? Also, some of us were experiencing hesitation issues that could be attributed to traction control and/or software related. A few have posted that a software update remedied the issue.
How is your battery doing?
If all else checks out, it could be the alarm module. I believe someone else on the forum had issues with the alarm going off, and the module was replaced under warranty.
Happy Father's Day!
Well...the "old" car was an MG TD that he had restored. He also drove a 450 SL. The family car was a special edition turbo Volvo station wagon with a factory sport tuned suspension, which was actually pretty fun to drive as a teenager. This was in the 80's.
What kind of wear pattern do your tires have...could be tramlining? Also, wider tires are prone to following imperfections in the road and can be exaggerated during braking.
Did you try applying pressure on the steering wheel (either direction and may need to try both), while hitting the start button (accessory position, without foot on brake)?