I will be taking a taxi from outside the main airport in Frankfurt. Will I be able to use a credit card to pay for the trip?
However, as the third link suggests, it's always worth checking with the driver first to ensure that a) they take credit cards and b) whether or not there are any fees associated with doing so:
Always confirm with your Frankfurt Airport taxi driver if they take credit or bank cards and if there are any card fees.
So short answer - probably, but check with the driver/company before you get in/book.
As first-hand experience from someone who lives in that city...
In theory, yes, definitely. This is standard.
In practice, a lot of taxi drivers will try to find an excuse so they don't have to accept payment by card (like "Oh, but you should have asked before, I don't have that machine on me"). I only had it happen once that the driver really couldn't handle the payment. In all other cases, it turned out being a lame excuse, and when I said I couldn't pay otherwise, it was suddenly possible.
By the way: The pickup price is fixed at €2.80 during daytime and 3.30 during the night (22-6h), regardless of how and where you get into the taxi (slightly lower rates in other cities, usually from 2.00 to 2.20€). They don't seem to be cheating with that, at least it hasn't ever happened to me.
Also note that when calling a taxi, the taxameter in Germany does not start when you pick up the phone, but when you board the car (by contrast, in France it seems to be "normal" that they start counting when the telephone rings, so you will not rarely have upwards of 10€ on the taxameter when you enter the cab if you called it by phone).
I've had someone try to pull off that one on me twice in 10 years.
Luggage does not cost extra (also contrary to other countries).