Partial filter warning light on

The glow plugs are only an aid to cold starting, and if you live in a mild to warm climate and you have a good strong battery and good compression, you often do not require glow plug warming. If the DPF has had a forced re gen burn and it has not done the job. I would be suspecting that the DPF has failed. If this workshop is BMW certified they should be able to run a diagnostic check to prove that the DPF is under performing and need replacing. One question, is the car showing any white smoke or excessive black smoke on heavy acceleration and overrun? This can be a clue to injector and fuel system problems as well.

No smoke at all, not even a little bit. I do not have loss of power.

That indicates that the fuel system is in fairly good condition. I would be ensuring that the workshop is qualified to diagnose the DPF as being faulty as if they get it wrong it will be an expensive mistake.

I was on my way to work, one hour later white smoke was filing the entire road and white smoke was coming through the air vents, but not from the engine. I turned it off and on again there was no smoke at all. The acceleration pedal was more of a sponge feeling with a fast response and a lot more power, I did put Cataclean in the tank so not sure if it is something I should be worried about or no.

Not sure, but I do not like using these wonder fixes in a can. I would let it go for a few days and see how it responds, maybe do a code check and clear just to see if anything has been set. If so do a clear, drive for a few days and re post what you are experiencing, and we will take it from there.