I think if the level is exact (say level 9.0) then it has no blue line. My drivers appear like this sometimes, and then after I train them their level is like 9.1 or something.
Staff do not train overtime, their only attributes that increase is Experience, morale and charisma. (Morale & Charisma is trained through doctor, and experience through time). Neither of those three attributes effect the overall.
Staff level does increase David. I have a commercial manager that was level 1 last season and is now at level 2.1 or something as there is a blue line along with the green line. I believe the staff only can increase their overall if you do well in the races and meet your team goals. I will say that it does take a long time to raise a staff member's overall by 1 so it's not really worth worrying about if you are progressing them or not.