Kermit -
No idea why the nosewheel is offset from the centreline, but may I offer a speculation on the second point? If the nosewheel is free-castoring, and assuming the centre of pressure is behind the pivot axis, it will of course "float" free to line up with the relative airflow. But behind a rotating pro, the relative airflow is actually skewed - cf. those ubiquitous diagrams of how slipstream "spirals" around the fuselage - so the lowest drag position may actually be with the nosewheel pointed off to one side.
A wind tunnel test (or some power-on then dead-stick formation flying!) would be an interesting test, but failing that rather extreme measure it might be interesting to "tuft" the nose of the aircraft with some strands of wool and gaffer tape and get an observer to see how the airflow lines up wit the engine running. Actually I suppose a partial tuft test could be done on the ground at, say, run-up power.