Hello, Car insurance companies typically total a car when it costs more to repair it than what the car is worth. Since it has already been totaled, it's highly unlikely that a car insurance company would be willing to give you full coverage (comprehensive and collision) for a rebuilt title vehicle.
When it comes to selecting your deductible you have to know what you can afford, and if you could cover the claim or damages with a high deductible. If so, high deductible + good driving = a lot of savings but a lot of people can't fork over 1k-2k in the event of an accident.
If the diagnostics are part of your car's repair and the other party is at fault, this expense should be covered by the insurance company. However, this is specific to your claim and you will need to contact the company that's paying for the claim to find out the specifics of what they will cover.
No, you would need to get a new policy since every policy needs to have the state minimum liability for Illinois and then you would be able to add comprehensive and collision coverage. Keep in mind, because of the age of the vehicle, there are some companies that will not add comprehensive and collision coverage. The Zebra can quote you with several different companies.