The LAN disconnects is a bit of a hit and miss, but it's definitely EIS, sometimes it happens, other times it doesn't.
For instance, I'm watching a stream/download a file, then I start a text editor (InType) on the first run, once EIS begins its probing, the stream goes dead/the file being downloaded aborts, nothing is coming in or out. Then momentarily later, though it varies on how fast the prompt window actually shows (sometimes takes ages to show). At this time connection with other programs will also be cut off and will only return to normality after the pop up window shows up.
As in regards to the last question, I think most of the long delayed prompts happen usually with outgoing connections rather than the incoming ones.