Credit Card Charge/payment

If you are going to do it - put it all on there and pay it off when the bill comes in.

If you cannot pay it all off in one month - you will pay interest on the charge that you did NOT pay. Not the full amount. You only interest on the balance being carried over.

If it were me? i'd put the whole thing on and pay it off in full when the bill came in. And putting it on the credit card protects you further. Check with your credit card company and see what they will cover if something goes wrong.

It depends. Some cards actually begin charging interest as soon as the charges hit, particularly if you are already carrying a balance. Some cards don't. I have one, that I can designate certain types of transactions that are called "full pay" transactions, that no interest is charged at all, if I pay it when they send the next statement.

If you have a card that has any sort of rewards program, I would just charge the entire amount, and then pay off what you already have towards the balance.
In fact, if you get a statement before you even charge the repair, I would go ahead and send in the max you can (including the amount "towards" the repair) so that you are having the maximum credit applied to your balance as soon as possible. (Fewer days of interest that way, and a lower "average daily balance" for it to be charged on).

I would pay for as much of it cash and charge the rest.

Check with your CC company to see what the grace period is on purchases. If you get one month before a purchase affects your average daily balance, then it won't hurt you. If you have no grace period, it will inflate your average daily balance for the next billing cycle and that will cause you to pay more in interest.

Any chance your bank or a credit union can give you a loan?

You have a repair that must be done. There is not a lot you can do to make that go away. Since this is a one time thing I would go ahead and charge it then make the payment.

Or I would draw out the cash from the credit card and pay cash for the entire amount. That way you have used all your cash and the withdrawal is not for very much.