Can you claim your car as a business expense if your company compensates you for mileage?

You can claim reimbursed mileage or the difference between what the company pays and the federal mileage deduction (Currently 54.5 cents per mile.

Say the company gives you 45 cents a mile that would mean you can claim 9.5 cents a mile.

If the company pays you 55 cents a mile, you cannot write off anything in addition

If they pay the IRS rate of mileage, you cannot claim any more. If they pay less than the IRS rate, you can claim the difference.

Only the amount in excess of your reimbursement

Not generally because the expense would be paid.

If the mileage compensation is including in your taxable income, yes. If not, then no.

Yes you can

No. You are either an employee or an independent contractor. You can't be both. If you are compensated for gas, you are an employee.

Maybe.

If your employer has an "accountable plan" and your reimbursement does not have taxes withheld, no.

If your employer has a "non-accountable plan" and taxes are withheld from the reimbursement and it shows up in your W2 with all other compensation, yes.