Yes, all of the wheel sprockets and motor sprocket that you listed will fit the E300 scooter.
The E300 scooter is factory geared for a 15 MPH top speed which may be the upper limit of the amount of speed that the stock 250 Watt motor can produce so we are not sure if increasing the gear ratio would result in a faster top speed with the original motor.
What do you mean faster? More top speed on flat pavement? The scooter is underpowered to start with so trying to get a higher top speed with only sprockets is asking for trouble if you need to climb any hills. I "geared" my E300S down to 9 MPH top speed (stock is about 15 MPH top speed), so that I could climb some fairly steep hills. I use 9 and 89 tooth sprockets with # 25 chain.
Without more information such as type of terrain, weight of driver, are you willing to accept LESS speed up hills..., I cannot make a recommendation.
As a side note, if you want more speed and don't want to change any sprockets or motor, just add 4 extra volts to make it 28V. That should give you about 2 extra MPH on flat pavement. I did this to my Razor E300S and my top speed went from 9 MPH to 10.5 MPH so that is a 1.5 MPH increase. However, it also increased power, torque, and fun factor. Now it goes up big hills AND can run along at a pretty good pace. It is not so easy to charge the 28V setup but I have a separate post on that. Just do a search for "oddball" and you will see it.
Our Motor Power Calculator shows that the maximum speed which can be obtained by a 250 Watt motor is 15 MPH, and with a 200-pound rider, the top speed is closer to 14 MPH. The restriction to being able to go faster with a 250 Watt motor is primarily from the air resistance encountered when traveling at the top speed.
The top speed with a 2500 RPM motor, 11 tooth motor sprocket, 36 tooth wheel sprocket, and 10" wheels is 22.82 MPH. The size of motor required to reach 22.82 MPH is calculated to be 754 Watts.
When installing a larger motor the distance between the motor sprocket and wheel sprocket will usually change so unfortunately we are not able to calculate what size chain would be needed for a modification like that.