Dopo ultimo aggiornamento windows 10 non riconosce più la licenza e non me la fà riattivare

The first error you pasted is a violation of the license policy. This means that you are suspected of using a Free License for commercial or business use. If you are using the application for personal use only, you can contact eM Client and explain your usage, then they may unblock the license.

If you are using eM Client for business use, you will need to purchase a Pro License.

I use a free license for my work, i am a technician at the university Federico II of Naples, Italy 

What i have to do?

Go to http://emclient.com/purchase-em-client to purchase a license.  You will then be sent a key that you can enter into eM Client by going to menu/help/license.  Please be aware that since you are not currently able to receive emails in eM Client, you will have to retrieve the license email from another client or web interface.

There is no need to reinstall eM Client.

Peccato, mi piaceva il client e non lo usavo per fini commerciali a di affari. Ne troverò un altro

If you are using it for your work and get some payment from the university, that means commercial or business use.