Monschau should not be under consideration as a base town for travel. It has no train station. Might make sense to stay in Aachen, which puts you 1 hour from Monschau by bus and just under one hour from Cologne by train.
"Gengenbach, Triberg, Schiltach and take a train ride on the Black Forest Railway"
The first two lie right on the BF Railway. Schiltach is on the Kinzig Valley Railway. There are direct trains from Gengenbach to both Schiltach and Triberg. Gengenbach is your best bet of the three towns mentioned, IMHO. Gutach, Hausach, Haslach, and Steinach, also on the BF Railway, might also work well for you depending on what you are looking for in the way of accommodations, town services, etc. We stayed in Steinach a number of years back at this farmhouse apartment with deck:
https://images.traum-ferienwohnungen.de/13558/1689120/46/hinteransicht-hofgebaeude.jpg
https://www.traum-ferienwohnungen.de/13558/
Staying in Freiburg adds a lot of useless travel time for these destinations, and you might need to make the trip twice to see what you have in mind from there, especially if the Vogtsbauernhof open-air museum in Gutach is on your list. It's the most interesting museum you can visit if you are interested in traditional life in the Black Forest.
At the time we were in Steinach, a studio apartment just the right size for one person, situated under the apex of the farmhouse roof, was available for rent as well. I don't see it listed on the site above now. But you might ask about it. I will send you a pm with Herr Schöner's email addresses if you wish to inquire about either apartment (which is how I booked there.)
If you want to visit Colmar, just travel there and spend the night.
Freiburg is also a nice city- with a population of roughly 240,000, so it's a vastly different kind of place than most people think of when they hear "Black Forest."
