You will not be able to use your ticket for any other trains than the ones listed on the ticket.
In practice however you can leave a train earlier than the stop listed on your ticket. And also usually enter a train at a later stop. It just has to be the exact train listed on your ticket. Usually they would just assume that you weren't checked in before and wouldn't think any of it. I would avoid telling the conductor this, as it is only asking for trouble. But it is doubtful they will ask or think anything. It is not unusual to be checked for the first time hours and several stops after being on a train.
You can also skip an entire leg. Because people will just assume you haven't been checked. Very normal. Happens to me all the time.
You would need an extra ticket for the Dortmund to Cologne stretch off course assuming your riding with a friend on another train and not on his car. Your ticket wouldn't be valid for this train.
This seems risky to do tough. Because trains in Germany are often not on time. So if you do this. Monitor the trains on the app to make sure you're not missing any of your connections.
Also you need to know that in the event that your original train runs more than 20min late you can use any train. This is not unusual to happen, because again trains often run late.