Is it alright to connect NC (no internal connection) to the ground?
This one is really clear, surprisingly clear in fact ... downright enlightened.   That additional wording that MicroChip put in ... "true ..." makes it a very safe bet that you can perform whatever routing function through that pin you wish to ease your layout.  The only caveat is not to put a sensitive net through the pin, since it will add parasitics (a handful of pF) if it matters.

Alternate wordings would be "DNC" for do not connect, which is a command, not a suggestion.  or "Reserved" where you must fear for your life if you ever connect that pin incorrectly.

I've been reading data sheets since the '70s and they have not been better or worse across time.  This one is very clear.

To convince yourself, put your meter on the highest resistance range to each pin in turn.  Checking that it declares over-range.  Make sure that you perform each measurement with both polarities of the meter.  Most meters use a one-polarity source, often ramping in a triangle, so they read differently each way and a diode will fool you.