Yep, as the other two posters said, the gear-shift animation is only used
when you're actually in control of the car, same with the***pit movement.
If people are burning you off on the straights, it could be because they got
on the power earlier coming out of the turn, or they could have a taller
fifth gear. Plus the cars vary in top speed, the Honda probably being the
fastest.
There is a skill to getting smooth quick gear-shifts though. Presumably you
are doing you own gear-shifts, which you need to do. In which case, as you
shift, lift on the throttle about 15-20%, and then straight back on full
power. It takes a while to get really good at.
Also, other drivers could be speed-shifting (not lifting at all), which is
obviously a little faster, not realizing it will brake their engine.
I don't think theres any need to mess with setups, just stick with the
default setup and reduce the fuel load to 5-8 laps for hotlapping. Monza is
an easy track, but because it has so few corners and so many fast sections,
you have to get every corner perfect to be fast. Also you will probably
find your are braking too hard and too early and turning in to the corners
with too little speed.
As for general advice on the Monza track, make sure you are flat out through
the left hander after lesmo 2. The two major braking points on the circuit
are before lesmo 1 and before Parabolica. You want to be braking after the
braking zone starts (the dark section on the track). Also the Lotus and
Eagle are good at Monza.