Chases are best done as opposed checks with the relevant skill (Pilot, Athletics etc). Determine the starting range bands of the parties to the chase. If the pursuer wins, they close a range band and vice versa.
I don't recall if there is any specific rule regarding shooting at vehicles with personal weapons (pistols etc). But treating hull trauma as x10 against these weapons is probably a good method, although I might let triumph hit one of the vehicle's critical systems. Also need to remember if there is shielding to take into account. However, if its a speeder weapon shooting at another speeder, I'd probably treat it as damage as written.
Firing weapons in a speeder chase, I guess the best thing to do is ask the PC what they're targeting, and what they're shooting with. They could shoot at the opposing driver etc or they might call a shot at the engines and try to disable or slow them down by shooting ahead of them into terrain, trying to knock something down. Think of it like the speeder chase scene from RotJ. And don't forget to add setback die