Yes, the latest cameras can shoot at blisteringly fast shutter speeds – but holding down the shutter button and being trigger ...
If your devices only support up to 4K at 60Hz, a "premium high-speed" HDMI cable (18Gbps, HDMI 2.0) is perfectly fine. Again, just avoid really old or thin cables. Early HDMI cables (HDMI 1.4 or older ...