Why do I have these connections? Are they a virus?

I have these connections. They show up under avast trace thingy. Are they viruses?

The DNS name for 157.56.98.55 is: bn1wns1011313.wns.windows.com

No, it's not any type of malware.

The reverse dns lookups lead to windows.com, deploy.static.akamaitechnologies.com., and bing.com, respectively.

The 1st and 3rd are Microsoft addresses and the middle is (I believe) a 3rd party helper type of address commonly found on lots of major websites. For more info about it: http://www.akamai.com/

Nothing to be concerned of (unless you value privacy, like me.)

Probably generated by your use of the Start search and/or Bing live tile.

You could always see connections well with this command prompt command:

netstat -ano

You can disable certain behaviors like this, I'm mostly sure. Look around the net or this website here at eightforums.com itself. Brink likely has an excellent tutorial on it, like practically everything there is, heh.