Fuel Injected Two Cycle Engine

So I know this topic has probably been covered, but I am complete amateur (hence why I am signed up here).

I am in charge of the Arduino and the programming aspect of the project to make sure that the fuel will fire from the hall effect sensor. I have done some research, but have no idea how to complete the remainder. I have about 4 weeks left.

Our senior project, our group decided to create a fuel injected engine from a Honda scooter engine. We bought a fuel injector, hall effect sensor, Arduino (UNO), and we are using a gravity feed for the oil. The Arduino is detecting the hall effect sensor and then the flywheel magnet will determine the firing of the fuel injector.

Can this be done? I've seen other projects out there with a similar concept...
What else do we need?

Thank you

No. If you only have 4 weeks and you are still asking if it can be done then you can't complete it in the time available.

Triject makes a really good ECU that works on two-strokes.

Don't 2-strokes use a premixed fuel/oil at a specific ratio
You will also need some form of pump system to provide pressurised fuel (or fuel/oil mix) to the injector.
How will you control or vary engine speed - ie sensors and an algorithm to measure air flow, calculate fuel required for that air flow, set injector duration to meet requirement etc

For timing you need to keep an estimate of rotation speed, then dwell angles can be turned into
delay times (delta angle = delta time x angular velocity)

Do a Google search for Speeduino and you will get an idea of the complexity of developing an Arduino EFI controller.