Is it permissible to contribute and donate from Zakat funds to a project for purchasing and expanding a mosque, and is it permissible to pay part of the purchase price "under the table" to the seller to evade state taxes, knowing that he requested an amount of 50,0 Euros in this manner?

It is permissible to build a mosque from zakat funds when there is a need and when donation funds are limited, especially in countries where a mosque is considered a necessity for Muslims. In such cases, it falls under the category of "fi sabilillah" (in the way of Allah). As for helping a seller circumvent laws, this is not permissible, because a Muslim must be faithful to the covenants and agreements they made upon entering those countries. Treachery and deception are not characteristics of a Muslim.