I have a 2005 A4 2.0 TDI S line

I absolutely love this car but have the following issues

When stationary at lights etc the car intermittently judders/ shakes to describe this accurately it feels like the whole engine block is moving causing the whole car to shake

There is a noise similar to a mouse occasionally coming from the back of the radiator I have examined the belts which seem in tact

The car seems to have a delay in starting at times having to turn over for several seconds before firing up

The most important point is that the car is really bad on fuel using 60-70% more than it should in an urban environment

Can anyone shed any light on these problems to save going to the local dealership initially