Yes, the default OpenFOAM solvers all use (pseudo) time-stepping, even for steady-state simulations so they will require significantly more iterations and time to converge than a dedicated steady-state solver.

Unfortunately, turbulence modeling is a science all by itself and notoriously hard to completely automate. Turbulence models are often tuned to specific flow regimes and situations, such as internal/external/separated flows etc. and can be very sensitive to mesh quality. However, the employed k-epsilon/omega models are historically the most widely used and therefore also tested so using them you should be able to at least get a rough idea of the flow behaviour as a starting point.

Leon Robers wrote

Thanks, using the Openfoam solver works!

Nevertheless, also for laminar flows it takes significantly longer to converge than the integrated FEATool solver (especially if one would choose the same stopping criteria). But I guess this is normal?

To simulate turbulent flow, can I confidently trust the calculated parameters for the k-omega/k-epsilon model? (I am not very experienced with turbulent flow at all)