1) - not sure (see 2)
2) - the tyre pressure warning system is very rudimentary and works off wheel speed and is usually measured via your ABS sensor. If it detects a speed anomoly, it will think your tyre pressure has changed. Could be a wheel bearing or similar and therefore links with #1 as it's confusing your ABS sensor.
3) Known issue with VVT. I let my glow plug light go out and wait a few more seconds before cranking. Sometimes helps, sometimes doesn't. Worse in cold weather.
4) Buy a Carista dongle and get VAG DPF app on your phone. You can then see the state of your DPF, when it is due a regen, performing a regen and also see how much `bottom ash` is in the DPF (basically how used/full up it is). A DPF light coming on suggests it is not completing a normal passive or active regen and can be a symtom of other issues. Not the end of the world but not to be ignored and for £30 you can monitor it yourself.
CARISTA