Does coffee affects the levels of serotonin, noradrenaline and dopamine?

Yes. The caffeine in coffee blocks Adenosine receptors, which when activated make you tired and sleepy. This blockade also affects all major neurotransmitters, such as dopamine, acetylcholine, serotonin -- and in high doses, norepinephrine too. Dopamine effects are not in the exact same regions of the brain that other addictive substances affect, though.