Why is mdns-discovery.exe always trying to access the network?

It is probable your admin checking there are no unauthorised things running in their network.
Or else you do not have a fire wall.

You really shouldn't post all that information about your network either or you might be getting the sack. Edit your post and remove the picture.erridicate those network numbers, edit the post agin and repost.

Anyway you posted in perhaps one of the two places on the forum you can't post a question concerning your project. You posted in the section for getting the IDE working, so I moved your post here.please be careful where you post in future.