Why do propellers on aircraft have a slight offset angle? Single-engine aircraft (one propeller on the 'nose')

Why do propellers on aircraft have a slight offset angle? I have picked up this information that the rotational axis of the propeller is not aligned with the roll axis of the aircraft, but I don't know why and by how much it is off. I also don't know the direction in which the propeller's rotation axis pointing (other than 'roughly' in roll axis direction).

Is the direction of the propeller's rotation axis important? 

Does the direction of the propeller's rotation have any influence on it?

How big are these angles between aircraft roll axis and propeller rotation axis typically?

Is this concept only useful for propellers?
The direction of rotation of the propeller introduces an asymmetry which designers try to mitigate by adding more asymmetries. Specifically, a right-turning tractor propeller (clockwise from the pilot's viewpoint) will swirl the propeller wake in the same direction which adds a negative sideslip angle on the vertical tail (which sticks up into the upper half of the wake only). By pointing the axis of rotation of the propeller slightly to the right (right sidethrust), this sideslip angle can be reduced.

Other means of correction like an incidence on the vertical tail would not work equally well: Once the engine is throttled back, such an incidence would require to re-trim the aircraft.

On multi-engined aircraft a sidethrust can help to reduce rudder input in engine-out cases. Here each wing engine points slightly away from the fuselage so its thrust will pull the aircraft into a helpful sideslip when the opposite engine has failed.

The propeller axis can also point slightly down in order to move the thrust line closer to the center of gravity, reducing thrust-related trim changes, and to reduce the P-factor effect (sideways shift of the thrust vector) at high angle of attack. This is called downthrust. One example would be the RR Griffon-engined version of the Supermarine Spitfire: When the new engine was installed, its lower thrust line required 2° more downthrust.

This is one of the few topics where the English version of Wikipedia stays schtum; only the German version has an article on it (Motorzug and Motorsturz).