Is it possible to ping through a NAT?
I don't see why not as long as the router/firewall allows outbound ICMP and the inbound responses.
It is quite possible, the router just has to allow it. I don't know that specific router though.
Yes. As long as the router allows the Ping request to pass outbound and properly tracks the request so that it can return. Most routers I have dealt with handle this correctly. Pings in though a Firewall (NAT or not) are often blocked.
There are tools which manipulate TCP packets to generate ICMP failures to provide the equivalent functionality through a Firewall.