It's possible that you may be incurring a surcharge for the out-of-state vehicle, but I don't know any company that currently employs this practice. However, the vehicle history you mentioned can change your rates.
Most insurance companies will charge more for a turbo engine if the VIN identifies it as such — since it has more power and speed, the risk of a claim is going to increase. The same goes for luxury or modified vehicles.
To my knowledge, no car insurance companies use ownership of the insured vehicle as a rating factor. The only way your premium would be impacted by having car loan is if the bank or dealership requires you carry additional coverage you wouldn't carry yourself for a vehicle you own.
There is no set dollar amount for a starting payment as rates vary by company and situation. It is common that your initial payment is more expensive if you were without insurance before you begin your new policy.