Is it permissible to report someone who falsely and deceitfully reported me for tax evasion, or to secretly take money from him equivalent to my loss?

The basic principle regarding taxes is that they constitute consuming wealth unjustly, unless the state's resources are insufficient to meet the needs of the nation. In that case, it is permissible for the ruler to impose them to the extent that suffices the purpose without injustice. At that point, it is not permissible to evade them. The ruling on evasion and reporting those who evade is based on this detail: if the imposition is permissible, then evasion and reporting are forbidden; otherwise, they are not. As for reporting with falsehood, it is forbidden in any case. The wronged person has the right to seek the removal of the injustice through legitimate means, and he has the right to recover his right in any available way if it does not involve injustice or transgression. If he wants to do that, he must be careful to be certain that he will only take his right or less. And the one who causes a wrongdoer to be tempted to take a person's wealth is liable for what the wrongdoer has wrongfully taken because of him.