You should rev match when downshifting, its better for the transmission.
It's better for MPG with LESS use of the gas pedal, so if you have to give it MORE gas in 3rd to keep the same speed as you would with LESS gas in 2nd, obviously you're wasting some in 3rd.
The car is jerky because you're too low in the RPM range and it's got no power, that's not good for moving parts in general because sometimes it can cause a shock.
Easiest way to conserve fuel is to accelerate slowly, shift at like 2500-3000rpms and don't break AS hard, I.E. only slow down as much as necessary so you only have to acclerate as little as possible. Accerating slowly/shifting early should keep you out of boost.