Neil Dickinsin

You will need to get it scanned and find the fault code, this will point to what the issue maybe but will need investigation and confirmation.

http://wiki.ross-tech.com/wiki/index.php/Diesel_Particle_Filter_Emergency_Regeneration

I fitted a k&n (as this will be less restrictive than a standard filter) to mine and also retro fitted the sock that comes with the standard filter(the sock washes out with detergent). I would also keep the standard airbox as this in my opinion is better than an induction kit as it keeps the hot engine air completely away from the intake. 

You should have a label on the drivers door showing tyre/wheel options and tyres, normally if you increase rim size and keep width you would need to reduce wall height also have you checked offset.

Yes

Mr muscle oven cleaner and T cut.

Don't forget MOT's have been changed last year for diesel emissions i.e. no visible smoke, so I hope you have a very good remap?

https://www.gov.uk/government/news/mot-changes-20-may-2018

Try https://en.m.wikipedia.org/wiki/ZF_8HP_transmission

Or try Rps online

Try Wikipedia as a starting point as this list information on different engines and gearbox combos. You need to decide if you want low tax or BHP then what your budget is. BITD 313 - 326 PS 650 to 700+Nm. These have tiptronic 8speed transmission. Tunable to around 400bhp.

The should be  J code and some other digits stamp on the inside if the rim.

M+S are winter tyres, I would fit the 215/55/16 the 55 means the tyre wall height in % of width. So running 205 tyres will give you a slightly smaller overall diameter so will show less mpg.

Just watched video and looks like water vapour of a cold exhaust on a cold day. 

Monitor coolant and oil level and if no change proberly worrying over nothing. 

Have you checked oil is not over filled? 

Try 7zap.com

I have just gone old school and fitted the old yellow stoplock that fits throght the steering wheel, also not leaving key in front door anymore as I have seen they blow torch upvc doors and put hand through to get key to brake into house to steal car keys. 

I choose these over the michalin for tyre noise only 68db, I also run tyres at 4-5psi higher then audi recomends 70psi back and 45 front (drivers door panel) as they felt a bit like jelly when driving hard, they seen alot better with higher pressure or it may be me expecting to much from them? (My tyres are 255/35/20) This is why I am going to try michalin next time. The wet grip is very good and a nice positive road feel, no tramlining as I had with the P Zeros. Also had 4 wheel tracking checked and corrected at ProTyre Fareham - very good, this stopped the front outsides scuffing that you get and the issue with rear tread edge scuffs across the tyre width. when you run flat palm over tread you can feel the tread edges a symptom of this when bad is it sound like a wheel bearnig is on its way out. 

I wouldn't fit P Zeros, I run goodyear f3, but next set of rubber will be Michelin pilot sport 4s.

Try your drivers door label for tyre and wheel sizes. You will need to keep them same offset.

7zap.com find part number and do a search. 

I use http://www.tyrereviews.co.uk/Tyre/ you can choose price, size etc.

7zap.com

My A6 heated mirrors work with the front demist and the door arm rest switch on either mirror position not the centre top position. 

Just buy an OBD read/write device and if You are happy reset the 'service due'.( as you must have saved a few penny's not getting Audi to service it?)

Try 7zap.com find OEM part number. Then enter into search engine. 

Are the brake calipers the same size?