In answer to your questions, no, no, no, yes, and no.
Your car would be registered as a passenger car or light truck, whichever it is. The registration will be the same for the vehicle, whether it is powered by gasoline, diesel, CNG, ethanol, electricity, or biofuels. (You can get some tax breaks and rebates for certain alternative fuels, but that does not affect the way the vehicle is registered.) The best plan is to get regular plates, but identify the power as electic. Once your vehicle is tagged as electric, the state will waive your requirement to emission test the vehicle. BTW, the registration no longer has the power source, but your title sometimes carries that description.
If you register your car as a passenger car, and do not tell them it is electric powered, they will require you to undergo periodic emission tests. If you fail to comply with the emission tests, they will start proceedings to suspend your license, so simply tell them it is electric, or even take it to the emission test facility, and they will certainly issue an exemption.
As to the insurance issue, there is no fraud in not telling your insurance company about the electric power, but I suggest you do, it saved me money. My insurance company knew about electric cars and trucks, and automatically wrote a discount since I only drive it shorter distances. It actually saved a substantial amount over normal pickup insurance in my case. My agent says the savings on trucks is quite substantial, as they know most electric trucks are not used in commercial service. There is apparently a savings for passenger cars, but not as big a percentage as trucks.
The registration (or licensing), and the rebate, and the emission test, and the insurance are four different issues, each with their own solution. None are terribly difficult, compared to building the vehicle.