Smoke coming from right wheel arch under engine - Cold Start

[PsYcHe]

The battery one could just be a spurious error.. they crop up all the time..

Just noticed a transmission mount error as well, that would cause roughness too. You may just have a connection loose, so worth checking them, or you may be unlucky enough to have two faulty glow plugs.

[a8starr]

I have just read my vehicle build spec and it states 'Without Auxiliary heater'. What else could be causing this smoke and bad smell?

[PsYcHe]

Just to double check, plug in VCDS and click on 'aux heater' and see if it works

Beyond that, not sure, but worth dropping the underfloor pan and checking.