Scalar fields can give rise to confined structures, such as boson stars or Q-balls. These objects are interesting hypothetical new "dark matter stars," but also good descriptions of dark matter haloes when the fields are ultralight. Here, we study the dynamical response of such confined bosonic structures when excited by external matter (stars, planets or black holes) in their vicinities. Such perturbers can either be plunging through the bosonic configuration or undergoing periodic motion around its center. Our setup can also efficiently describe the interaction between a moving, massive black hole and the surrounding environment. It also depicts dark matter depletion as a reaction to an inspiralling binary within the halo. We calculate total energy loss, and linear and angular momenta radiated during these processes, and perform the first self-consistent calculation of dynamical friction acting on moving bodies in these backgrounds. We show that the gravitational collapse to a supermassive black hole at the center of a Newtonian boson star (NBS) is accompanied by a small change in the surrounding core. The NBS eventually gets accreted, but only on times larger than a Hubble scale for astrophysical parameters. Stellar or supermassive binaries are able to "stir" the NBS and lead to scalar radiation. For binaries in the LIGO or LISA band, close to coalescence, scalar emission affects the waveform at leading -6 PN order with respect to the dominant quadrupolar term; the coefficient is too small to allow detection by next-generation interferometers. Our results provide a complete picture of the interaction between black holes or stars and the ultralight dark matter environment they live in.