No, a brushed controller will not work with a brushless motor, I'm afraid.
Also, speed is generally a function of battery voltage and motor Kv, so increasing the current doesn't normally have much effect. As a general rule, more current means better acceleration and hill climbing, more voltage means more speed. There are some exceptions, such as when the speed is being limited by the motor power at full throttle, but they're a good general rules.
If you swap the motor for a more powerful one, and swap the controller to match it (which may not be that straightforward, as some scooters run a lot of the other, non-motor related, electrical stuff through the controller) then you may or may not be able to get a bit more speed, depending on the Kv of the motor you choose and the ability of your battery pack to supply the required power.
Please ask questions on the forum, rather than by PM, as it helps others and you'll get a better range of answers.