1.8 TSI / 2.0 TSI   4x4

The wife's car has suddenly started to make a "buzzing" noise/sound after turning the car off.
Can last up to about 2 minutes.
The noise seems to be coming from the electric fuel pumps in the tank !?!?
What and why has it suddenly started making this buzzing sound ? 

Could be the fan?  That's the only sound I've ever heard after turning the engine off, if it was partway through DPF regeneration at the time.

An electric coolant run on pump runs for at least 1 minute after the engine is turned off.

 

Open the bonnet and you should be able to see coolant being returned to the reservoir via the small pipe at the top. If the engine is cold  and safe to do so, you could remove the reservoir filler cap and its easier to see the coolant  returning.