Deutsche Bank ATMs in Ahr, Mosel and Rhine Valleys

I'm not sure about your specific question about DB ATM's at FRA, but I will offer this:

even if there are some DB ATM's at the airport, Frankfurt is a huge, cumbersome airport
and finding a specific bank's ATM is not going to necessarily be easy, especially if you
are trying to make a connection.

I can say that there are plenty of ATM's scattered throughout the secure passenger areas
so you should have no problem finding one. Someone else can probably give more detail,
but there are a lot of "fee-free" ATM's now, so you may not need a DB one to avoid fees.
You can always stick your card in and then xcel the transaction if you don't want to pay a
fee. Although, in the bigger picture, if you decide you need cash in your pocket, the ATM
fee is a relatively minor annoyance.

There are Deutsche Bank ATMs all over the Frankfurt airport. Often right when you come out of the arrival gates. You will have no problem finding them. They are not difficult to find.
Yes, you will need cash in the small towns.

In Google maps, type Deutsche Bank, the city you’re interested in and you’ll get a result saying something like Deutsche Bank near Bacharach. For the three towns you mentioned, the answer is no Deutsche Bank ATMs.

There is a Deutsche Bank in Trier, Bernkastel-Kues, Bingen am Rhein, and Koblenz. Most places we went to in the Rhein and Mosel areas accepted credit cards, however, some had minimum purchases between 5-15€ to use one. When I wanted Euros I picked them up when we were in a town with a Deutsche Bank, e.g., Baden Baden and Bensheim. Prior to our trip I bookmarked the Deutsche Bank ATMs in the areas we were traveling on Google maps. That made it easy to find them.