I seem to recall that an inbound ping to a static NAT is responded to by
the NAT rather than being passed to the internal host. That was a while
back so maybe it has changed...

My question today though is if I ping outbound via NAT to an Internet
host - does anything strange happen or can I say with certainty that any
statistics I collect on uptime of that host are accurate ?

Yes, I am arguing with an ISP !