Ciao Emanuele!
If you seem to be experiencing ranking issues, the best way you can see if there is something to worry about or not is by seeing if there have been any drops in organic sessions on analytics. Has there been a drop?
If there is a pattern to the types of keywords which you seem to not be rankng for, you should check in analytics to see if the pages on your site which correspond to the keywords are losing organic traffic or not. Example: keyword A will be most relevant to example.com/page-a
Search results are different for different users, based on location, which version of Google you are using, whether you are signed in to Google not etc. so don't be too concerned unless traffic is also affected.
Additionally, the message in GWTs on 12/6 isn't something to worry about. I have also seen this message for many of the sites I manage and it is really just Google giving some tips such as defining a target country, giving access to other users, creating XML sitemaps etc.
Let us know if you are also experiencing drops in traffic!