Some have used a service called Plastiq, but only worth the 2.5% fee if you opened a new card and are REALLY going after some bonus worth more than 2.5% of your down payment... Typical CC rewards are 2%.
No. They only let you pay the initial $2500 by credit card. The bonus cash or miles that everyone is after come out of the percentage of the transaction that Tesla pays to the credit card processor. The company is well aware of this, so they limit the amount that you can pay by CC. The balance must be paid by check or wire transfer.
I financed through my bank, but when they cut the check they calculated wrong and were short by about $700. My Delivery Advisor noticed it and I just paid the difference with my card. So maybe in certain circumstances, you can use a CC.