I would like to stay in Italy for a few days after which I would prefer going to Finland for a week and then back to my country (non - EU citizen). I was wondering if the Finnish authorities wouldn't mind me entering their country even though my visa was issued for Italy rather than Finland and whether they would question me why didn't I stay in Italy for a longer period of time before entering Finland? Generally speaking, I would like to find out what is Finnish border control like (whether they are too strict or not)?
Your "Italian" visa is actually a Schengen visa valid for the entire Schengen zone. Since Finland and Italy are both in the Schengen zone, you can travel to both, and there is no border control at all between the two countries.