daox,
the schematic looks good to me from a conceptual point of view.
In the event that you have depicted all the components you plan to use you may have an issue or 2
If you have depicted the transistor setup as you intend to use it then it may not work depending on the output of the arduino and type of mosfet.
if you have a high side switching fet (i think it is p channel) it will conduct if the voltage between the gate and the source is below the Vgs specified in the datasheet. It appears that you have connected the source pin to 12v. I assume the arduino has a 0 or 5v output. So when you want the mosfet off, the arduino will output 5v but the vgs will be 12-5 which i 7 which is typically enough to conduct the mosfet.
For the reason above you will either need a low side (i think its N channel mosfet) and switch the ground of the solenoid or you will need to use a transistor and resistors on the high side mosfet to deal with the control voltage level shifting. I would draw a picture but dont have too much time right now sorry. This can be a resistor (say 10k) that goes between the gate and source, then a bjt transistor which can be controlled by the arduino without level shifting can be used to pull the voltage down on the gate of the mosfet.
This brings up another point, you will want to check that the solenoid that is bridging the ignition switch will tolerate 12v and that the solenoid that breaks the connection between the crankshaft sensor and the ecu will activate off the 5v from the arduino
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