There is no date related info on a VCDS scan relating to s/w updates (only on fault codes) so I'm unsure if there is a DTS indicating when software was installed, however the Audi diagnostic kit is more sophisticated, so that may show date info.
Regarding TD1, that's not a flag generated by carrying out an engine scan, that's an administrative flag set by Audi on the cars electronic record card, which is presented to any dealer who services the car.
The reason Audi can detect if there has been an unauthorised software flash on the ECU, is that there is a "flash counter" within the ECU. So if the counter says the ECU has been flashed 5 times, but the cars VAG electronic record says it's been dealer flashed/updated twice, then they know someone outside of the authorised dealer network has been playing with the software. This is the primary reason that "flashing back" or returning to stock ECU software does not guarantee you will not be caught and flagged TD1.
You could try to find an independent garage, with dealer level diagnostics, to take a look-see.