Has someone tried to change the timing of the engine by moving the sensor back and forth ? It has a little provision to advance or retard. Is this to fine tune the engine or is it better not to touch it at all ?

I would recommend not touching it at all.

Timing change as a means of getting more performance is vastly over rated..If an engine would run better with more advance the manufacturer would make it that way....Same goes for larger carburetors...A BIG carb will sometimes help, usually not worth the effort..My G26s run almost the same with a little 3/8 carb as they do with the too large (IMO) stock one...
Move it against the direction to advance, with rotation to retard..You will likely see little, if any, difference...Been there

Sage advice from the other posters.
If it ain't broke, don't try to fix it.
If you want more power trade it in on a bigger engine.