In the past years, we have undertaken an extensive investigation of LMC and SMC star clusters based on HST data. We present photometry and astrometry of stars in 101 fields observed with the WFC/ACS, UVIS/WFC3 and NIR/WFC3 cameras. These fields comprise 113 star clusters. We provide differential-reddening maps and illustrate various scientific outcomes that arise from the early inspection of the photometric catalogs. In particular, we provide new insights on the extended main-sequence turn-off (eMSTO) phenomenon: i) We detected eMSTOs in two clusters, KMHK361 and NGC265, which had no previous evidence of multiple populations. This finding corroborates the conclusion that the eMSTO is a widespread phenomenon among clusters younger than ~2 Gyr. ii) The homogeneous color-magnitude diagrams (CMDs) of 19 LMC clusters reveal that the distribution of stars along the eMSTO depends on cluster age. iii) We discovered a new feature along the eMSTO of NGC1783, which consists of a distinct group of stars going on the red side of the eMSTO in CMDs composed of ultraviolet filters. Furthermore, we derived the proper motions of stars in the fields of view of clusters with multi-epoch images. Proper motions allowed us to separate the bulk of bright field stars from cluster members and investigate the internal kinematics of stellar populations in various LMC and SMC fields. As an example, we analyze the field around NGC346 to disentangle the motions of its stellar populations, including NGC364 and BS90, young and pre-MS stars in the star-forming region associated with NGC346, and young and old field stellar populations of the SMC. Based on these results and the fields around five additional clusters, we find that young SMC stars exhibit elongated proper-motion distributions that point toward the LMC, thus bringing new evidence for a kinematic connection between the LMC and SMC.