Star formation rates and morphologies of galaxies, particularly low-mass galaxies, are strongly linked to the properties of their environment. Using a large sample of galaxies in SDSS groups, we investigate the dependence of star formation and morphology on host properties such as the X-ray luminosity and dynamical state, while controlling for stellar and halo mass. We find that galaxy populations in groups with strong X-ray emission have preferentially low star-forming and disc fractions, both within and beyond the radius associated with the X-ray emission. Additionally, we consider the effect of group dynamics on the properties of member galaxies and the infalling galaxy population separately. We show that the fraction of both star-forming and disc galaxies are independent of dynamical state for galaxies at large group-centric radii, while galaxies within the inner regions of the halo are sensitive to the dynamical state of their host group. Specifically, low-mass galaxies in unrelaxed groups show higher star-forming -- though no difference is detected when considering disc fractions. Together these findings help constrain the mechanisms at play in environmentally driven galaxy evolution.