Its normal to ask for credit card info or payment info of some kind.
during a normal sale, there are several people or companies who provide services to you. They normally get paid at closing by the title company (that's all part of the "closing costs" that you pay), but if the deal falls through for some reason, they still have a right to get paid for the service they provided.
This might include an inspector, appraiser, attorney, title search, or other services.
For example if the appraiser does their job and gives you & the bank a proper appraisal, but you back out the day before closing, that appraiser has the right to be paid for their work. So they would charge your credit card for the appraisal fee.
So that much is perfectly normal and you should go ahead and provide a CC number. Your card won't be charged for anything as long as the sale goes through as planned (in which case all those fees are wrapped up in the closing costs and paid by the title company using the money you provided to them).
I don't understand what the purpose of the domestic partner form is though. If your wife is not on the loan or the deed then I don't know what that would be about. Ask your mortgage company for more info, perhaps it was a mistake.