Ok so for the first part, lets say you run one of the numerous speed/quality tests for your internet line. By default routers are set to invisible so that others can't ping them, for security purposes, and the testing servers kind of need it in order to determine how good your line is. Explained in a bit more detail here:
http://www.dslreports.com/faq/962
On mine, in order to become ping-able, you enable WAN ping response. On mine that's under Advanced->Advanced Network. Not sure where it would be on yours.
I wouldn't touch IGMP. Not sure what it is. QoS is only important if there's lots of traffic at your home, (others watching netflix, browsing, streaming) and you're trying to prioritize your voice chat over everything else. Typically I don't touch this either as I have no need to and I'm assuming for testing purposes, neither do you (hopefully whoever else is using your connection isn't doing so when you're testing it). Only look into it if others on your network take up significant portion of its traffic.