Screen resolution and camera quality usually determine the picture in my experience.
To a certain extent yes although you have to remember that we're talking a digital image here not a negative. Being digital the raw data captured (raw data cannot be visualised) needs to be processed and turned into a visual image. During this process, the signal captured by the tiny sensor needs to be amplified at which time noise suppression also takes place. It is often this noise suppression software that marks out a good camera and very often, good software too - I'm thinking Adobe Photoshop here. In the case of the pictures linked to earlier, the first image is degraded and the software (firmware) has not done a very good job of suppressing the noise whilst in the second, the noise suppression is much better. With very low light levels much greater amplification is need and hence noise suppression because after all it's not like a normal camera having a flash available
As a rule - greater signal amplification results in greater noise which needs suppressing. Too much suppressing and sharpness deteriorates. I'm sure that a Canon 100mm lens placed on the back of the car would also produce a much better image but whose going to pay to have that fitted?