Can diagnostics tell when a fault started

In a word, no

Ah thats a point, was think you wanted a date \ time

My scanner is not up to much, but I don't mind taking it somewhere and paying if it means I can prove that they were aware the fault was there when I picked the car up. Also we have noticed the engine management light does not come on when limp mode starts, we suspect it may have been tampered with.

What year is it? Because if it's pre-2000 it probably won't have the MIL enabled even though it's actually present in the instrument cluster. It wasn't a legal requirement in Europe until then. If it's later and it is enabled it should do a lamp check for a couple of seconds when you turn on the ignition.

Not all fault codes necessarily turn the MIL on. The MIL light comes on if there's a fault that will cause an increase in emissions. Limphome is usually only triggered by safety related faults. Some faults will do both.

No. They'll simply have cleared down the memory and its not recoverable on a VAG. Blame all the sensors they chuck on them that constantly error, but the first thing any mechanic does now is print off the error codes, clear it down and then test drive it to see what new errors register.

The other reason they do this is to avoid chasing phantom errors, my golf was giving me problems with the sensors but the fan sometimes gave an error probably due to age, it worked fine. So you'd stack up errors (of the type you don't see on the dash) and a car in 4 years may log 20+ of these. Mechanics don't want to wade through it all. In all honestly if it's VAG and limp mode related the odds are the PO flogged it because it's ball breakingly expensive to cure any remotely modern VAG (edit: VAG sensor/limp mode problems, the mechanicals are still good!), even VW struggled with some issues on mine.