Carbine accuracy is not always an improvement over handgun accuracy.
Some handgun ammunition is going to be a 8″ grouper at 100y regardless of what it’s being
fired out of. I’ve had opportunity to shoot a decent number of rounds out of bench guns testing ammo
at extended ranges and many pistol loads are not up to the accuracy requirements some of us need.
Increased velocity generally, but not always, again it depends on the load and pressures involved.
Range is generally increased more by the increased sight radius or optics than by barrel length.
Effectiveness? Again, this can vary. Bullets, especially expanding bullets are built to function within a particular parameter, too little velocity means little or no expansion, too much velocity means too much expansion with reduced penetration and possible bullet blowup.
Carbines are easier to make hits with beyond normal ranges, and are certainly easier to arm less trained persons with, but you are still stuck with the limitations of the gun and ammunition, just recognize the strengths as well as weaknesses of the gun/cartridge.