||The second sounding-rocket flight of the High-Resolution Coronal Imager (Hi-C 2.1) provided unprecedentedly-high spatial and temporal resolution ($\sim$200 km, 4.5 s) coronal EUV images of Fe IX/X emission at 172 \AA, of a solar active region (AR NOAA 12712) near solar disk center. Three morphologically-different types (I: dot-like, II: loop-like, \& III: surge/jet-like) of fine-scale sudden brightening events (tiny microflares) are seen within and at the ends of an arch filament system in the core of the AR. Although type Is resemble IRIS bombs (in size, and brightness with respect to surroundings), our dot-like events are apparently much hotter, and shorter in span (70 s). Because Dot-like brightenings are not as clearly discernible in AIA 171 \AA\ as in Hi-C 172 \AA, they have not been reported before in AIA 171 \AA\ images. We complement the 5-minute-duration Hi-C 2.1 data with SDO/HMI magnetograms, SDO/AIA EUV and UV images, and IRIS UV spectra and slit-jaw images to examine, at the sites of these events, brightenings and flows in the transition region and corona and evolution of magnetic flux in the photosphere. Most, if not all, of the events are seated at sites of opposite-polarity magnetic flux convergence (sometimes driven by adjacent flux emergence), implying flux cancellation at the microflare's polarity inversion line. In the IRIS spectra and images, we find confirming evidence of field-aligned outflow from brightenings at the ends of loops of the arch filament system. In types I and II the explosion is confined, while in type III the explosion is ejective and drives jet-like outflow. The light curves from Hi-C, AIA and IRIS peak nearly simultaneously for many of these events and none of the events display a systematic cooling sequence as seen in typical coronal flares, suggesting that these tiny brightening events have chromospheric/transition-region origin.