Is it normal for a car to burn/consume oil ?

Turbo failure.

I was being serious.

There's a few factors to consider...
On one hand you've got an engine that is clearly burning oil since we've established it's not leaking.
It's not in the first flush of youth so tollerances will now be much greater than when it was first put together.
Fully synthetic oils tend to have high detergent properties. At this age and mileage there will be a fair few carbon deposits clinging to the oil passageways. You run the risk of dislodging these deposits and them subsequently blocking an oil gallery if you use a fully synth oil. You may think you are being kind to the engine but if the above scenario were to happen you'd starve the top end of oil and it would grenade.
On the other hand as CB points out using the wrong spec oil means that the additive package just isn't there for the bearing surfaces of components such as the turbo. However, the viscosity index isn't neccesarily linked to whether or not the oil will meet specs in terms of the additive package
Another point - you mentioned further up the page that it had been run practically dry of oil... well that won't have helped.

If it meets specs in terms of the additive package you can try a slightly thicker oil. This may well stop it burning what you put in.
Or, you can just keep feeding it as and when.

I take it you still haven't fixed your MAF yet? Unlike a petrol that gets super hot when the AFR is lean, diesels actually get excessively hot when overfueled and that won't be helping your oil consumption...

On the other hand as CB points out using the wrong spec oil means that the additive package just isn't there for the bearing surfaces of components such as the turbo. However, the viscosity index isn't neccesarily linked to whether or not the oil will meet specs in terms of the additive package