Connect signals to N.C pins in diode array (for ESD protection)
When listed in a datasheet, "No connect" can mean "Don't connect this pin!" or "We didn't connect this pin.". This looks like the latter. The 0.6 pF is just parasitics, and picofarads will not affect a UART or reset.

Your problems are most likely unrelated to these connections. Since you're seeing differences between copies of supposedly identical boards, there are probably manufacturing or assembly defects (but this isn't 100% certain - could also be marginal design).  I would start with a thorough visual inspection under a microscope looking for soldering shorts and opens. Check polarity / pin 1 position of all active devices.

Maybe when you removed this part from your defective boards, you also reflowed some other nearby parts.