Using density functional theory, we investigate the electronic and magnetic properties of 3d transition-metal adatoms adsorbed on a monolayer of Mn on W(110). Mn/W(110) has a noncollinear cycloidal spin-spiral ground state with an angle of 173 • between magnetic moments of adjacent Mn rows. It allows to rotate the spin orientation of an adsorbed magnetic adatom quasi-continuously. Therefore, this surface is ideally suited for manipulating the spin direction of individual atoms and exploring their magnetic properties using scanning tunneling microscopy (STM). The adsorbed V and Cr transition-metal adatoms couple antiferromagnetically to the nearest neighbor Mn atom of Mn monolayer while Mn, Fe, Co, and Ni couple ferromagnetically. The magnetic moments of the 3d adatoms are large and show a Hund's rule type of trend with a peak in the middle of the series. We find large spin splitting of the 3d transition-metal adatoms, large spin polarization of the local vacuum density of states up to 73% at the Fermi energy, and significant tunneling anisotropic magnetoresistance enhancement up to 27%. We conclude that such large values stem from the strong hybridization between the adatoms and the Mn atoms of the monolayer. Furthermore, identification of spin orientations of the adatom using spin-polarized STM is only possible for Co and V adatoms.