jeez dude, where do I start
If I were you I would get it to a decent VAG garage asap to get some proper diagnosis on it?
if the oil light keeps coming on, then clearly its very low on oil, probably due to the blue smoke bellowing out, its obviously leaking from somewhere, hence the loss of oil and oil light
if its not boosting and you have blue smoke then yes I would at best say the turbo has gone bang, probably oil pissing out the oil seals and god knows where else
have you looked around the turbo to see if there are traces of oil, or where you park it at night, see where the oil is leaking from onto the floor?
also how can you say the car drives fine.....the car is meant to have a turbo, so you are saying a turbo aspirated car with a knackered turbo drives fine?
how did you diagnose the turbo shaft has snapped? unless you take the turbo off the car or have x-ray vision then you wont know what is wrong with the turbo unit
I wish you the best of luck, but if you knew it had issues, why did you buy it?