Experimental realizations of charged ions and neutral atoms in overlapping traps are gaining increasing interest due to their wide research application ranging from chemistry at the quantum level to quantum simulations of solid state systems. In this paper, we describe our experimental system in which we overlap a single ground-state cooled ion trapped in a linear Paul trap with a cloud of ultracold atoms such that both constituents are in the K regime. Excess micromotion (EMM) currently limits atom–ion interaction energy to the mK energy scale and above. We demonstrate spectroscopy methods and compensation techniques which characterize and reduce the ion’s parasitic EMM energy to the K regime even for ion crystals of several ions. We further give a substantial review on the non-equilibrium dynamics which governs atom–ion systems. The non-equilibrium dynamics is manifested by a power law distribution of the ion’s energy. We also give an overview on the coherent and non-coherent thermometry tools which can be used to characterize the ion’s energy distribution after single to many atom–ion collisions.