I have recently replaced the fuel filter and added a fuel additive of my Cayenne, both are bought from Porsche company, but the very next day I drove my car and it starts to stumble and stalls. Would this be a clogged injectors and how can I resolve the issue?
There are a few potential issues as far as I can see. I'm drawing from my own experience with fuel systems and from a few of the comments.
First, is/was your tank full when you put in the fuel additive? Fuel additives should always be mixed into a full tank of gas. The best way to add it is have a half tank, add the additive, then top the tank up. You need to have it diluted by the gas. If you indeed have less than half a tank, try filling it all the way up to make sure the additive is diluted and mixed in with the fuel.
Next, double check all of the connections you fiddled with. Check that your connections are fuel-tight, and that none of the hoses accidentally got holes in them. Even a small bit of air or fuel leakage can cause major problems. I know you said you checked them, but check again.
Finally, make sure your fuel filter is the right way around. They only work in one direction, so make sure that it is oriented correctly.
Hope this helps!