Well, either that wasn't true, or is not true anymore.
As you told me, I now removed all of the 0.0.0.0 entries from the hosts file and then rebooted the phone. This did not cause any change to the strange effect. But to tell the whole story, before I applied the changes to the phone I already had blocked these sites by means of the child protetection blacklist within my router. So my conclusion still is, that something (not necessarily QNetMan2) really is trying (in vain) to establish a connection with doubleclick.net. What do you think?
Please do everyone (trying to help you) a favour and remove all entries but the first one from /etc/hosts. At least temporarily. Once you confirm that your "issue" is solved you have your answer, the thread can be closed, and you can continue polluting your /etc/hosts with invalid data.