@ Georgi27
Well your avast alert window indicates that it is running (for whatever reason), as the process responsible for the connection attempt is that in your attached image.
I don't know if this is some update attempt/check, but the destination URL is somewhat obscure if it were an update check, etc.
You could check if there isn't some scheduled task for skype.
You could also try uninstalling skype as a check to see if the Avast alerts cease.
Note: Given Michael's post, yes it could be malvertising (malicious 3rd party ads) and could be a false positive. How to report this as a false positive isn't going to easy, as I mentioned I didn't get an alert on a direct connection to the domain, nor is there an avast alert on skype.exe
But my point is still this, why would skype be responsible for the connection, when as you say it isn't meant to be running (on startup). Yes many free programs have in app/process ads, but the key here is in the app/process if it isn't meant to be running.