The error code in Address 01 is because of the error in Address 03. The error code in Address 03 is because the battery has been disconnected. Once you drive the car for a short distance the code won't register anymore, but you will still have to go in afterwards and clear this DTC.
The error code in Address 61 may be caused by a faulty alternator. Check out the following page and in particular to the Service part, number 2. Not saying this is the cause, but worth at least investigating if only to eliminate it. I was wondering that since you initially lost A/C and power steering, both of which are driven by the serpentine belt and that also drives the alternator, it may be the alternator, assuming of course that there are no seized pulley or broken tensioner.
https://workshop-manuals.com/audi/a6...ulator/270606/
With the error code on Address 09, because it's intermittent, difficult to say what it could be. I'd focus on the other things first, clear the codes, and see if Adress 09 throws the same error again.
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2001 A8 D2 FL 3.7 Q - LPG Conversion, Engine: AKC, Gearbox:FBB, Colour:LY5X Aqua Blue pearl effect, Interior:WJ light beige/dark beige valcona leather with burr walnut inserts
My DIY jobs -
Replaced alarm horn,
Replaced Coolant Temp sensor,
Updated RNS-D firmware,
Installed Reversing Camera and Digital TV,
Dashcam Installation,
Retrofitted Rear Blinds,
Auto-Dimming Rear View Mirror,
Chrome Boot Struts
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2008 S8 D3 5.2 V10 - Engine: BSM, Gearbox:KLW, Colour:LY7F Suzuka Grey Pearl Effect, Interior:Black/Black with Silver/Black valcona leather with carbon atlas inserts, Bang & Olufsen, Heated windscreen, Soft-close doors, TV, DAB, AMI, Quad Zone, Auto Boot, Auto dim Mirrors, Keyless entry, PDC with rearview camera, AFS II Headlights
My DIY jobs -
Fan Jet Windscreen Washers,
Retrofitted Electric Side Blinds