I believe there are multiple conflict situations in this case. It is definitely an overwhelming Monday. 🙂 What I would do in this case i just take seconds to prioritize things. First, I would communicate to my coworker that I currently can’t respond to his/her text becasue I have a customer. Second, I would turn attention to this customer. Of course, the most important thing is to understand why the service did not work. Politely, I would ask questions, and I would listen to the problem so we can find the solution together. Regardless of paying back the money, treating people with respect and understanding is crucial to the reputation of any company. If I can’t solev the issue I would turn to a superior for help of course.
Third: the common project with the coworker would be hard to resolve, but regardless of the tension we have to focus on getting things done. So I would communicate really clear of what I need from him for the project. I would definitely avoid direct conflict before submitting the project, and I would keep interactions to the necessary. After we finished,maybe, we can discuss with more openness, since we are under less pressure
As an athlete I faced many similar situations. I often had to let go of my ego, or my need to be right, because the goal of the team and our work togteher was more important. Although I did not clarify the conflict at the end.