Getting from Mülheim to city centre is easy. Take tram no 4 from von-Sparr-Str to Neumarkt and then walk to old town. As for tickets: day pass for city soil is 8,50€ and group day pass for up to 5 is 17,20€ . So if more than two in your group the group pass would do. You can buy tickets on the tram by card.
When arriving from Brussels at Cologne central, take no 18 from Breslauer Platz to Mülheim Wiener Platz. You’ll arrive subway. Go upstairs to ground level and take no 4 to von-Sparr-Str, it’s two stops from there.
Generally I would not bother too much about tickets as city will be packed with fans 😎