It checks how fast your connection is to each hop on your route to the cf server. The lower the better, and anything below 250 ms is perfectly fine.

The reason you time out on #2 is that your modem ignores the ping requests on purpose.

I don't know how new you are to muds, but on carrionfields and most other muds, some commands lag you, i.e. your next command will not go through for a certain amount of time. For example if you wheel kick something, it'll be roughly 5 seconds until your next command goes through. Are you sure that isn't the issue? I'm asking because you said that it mostly happened in combat.

You could also try downloading ytin at http://ytin.sourceforge.net
It's a very basic mud client that should run smoothly on pretty much any computer.