I'm going to trust Michelle on the way the IRS is doing the credit. However the tax software manufacturers are already working on somehow making this credit work. The declining balance nature of the credit doesn't make any sense to me, at least in terms of getting folks into hybrids, but it is the nonsensical way the Congress decided to do it this year.
You can finance a car just about any way you want. Including having both yourself and your fiance on the note and security agreement. However with a car, which is personal property, I wouldn't do that, unless you absolutly need both of your incomes calculated into the lending equation to be able to qualify. If you have to do that, well, I'm not so sure that you should be buying a new car because your debt load at that point is huge.
Depending on what state you are in you may not be able to place both of your names on the title. That may also complicate the lending process as one of you holds title and the other does not, but both have a debt obligation. That is an unadvisable situation.
As for the tax credit, until you two are married, you cannot file jointly. That means one of you can claim the credit and the other cannot.
At this time, I think it is advisable that one of you do the purchase of the vehicle, by having the car placed in one name, having the lending done in one name and fileing for the tax credit under the person who holds title and the loan.
As for vehicle delievery times. Shop around, widen your search radius, find some rural dealers. Rural dealers may have units on the lot waiting to be sold and rural dealers may be able to order in the exact vehicle you want in a shorter period of time than an urban dealer.