Magnetic proximity effects in single-crystalline NixMn100x/Ni(/Co) bilayers on Cu3Au.001/ are investigated for in-plane (IP) and out-of-plane (OoP) magnetization by means of the longitudinal and polar magneto-optical Kerr effect. Attention is paid to the influence on concentration- and thickness- dependent antiferromagnetic ordering (TAFM) and blocking (Tb) temperatures as well as the exchange bias field (Heb). For all the NixMn100x films under study in contact with IP Ni, increasing TAFM is observed with decreasing Ni concentration from 50 to 20%, whereas only a slight change in TAFM is observed for the OoP case. Between 28% and 35% Ni concentration, a crossover temperature exists below which TAFM for the IP samples is higher than for the OoP samples and vice versa. Tb is higher for the IP case than for OoP, except for an equi-atomic NiMn film, while Heb increases significantly for both magnetization directions with decreasingx. These results are attributed to: (i) a rotation of the non-collinear 3Q-like spin structure of NixMn100-x from the more-OoP to the more-IP direction for decreasing Ni concentrationx, along with an associated increased magnetic anisotropy, and (ii) a smaller domain wall width within the NixMn100-x films at smaller x, leading to a smaller thickness required to establish exchange bias at a fixed temperature.