Should the person whose possessions were stolen while performing i'tikaf be given money from what is found in the mosque under the carpets, according to his estimation, and the remainder be given as charity to the mosque?

It is not permissible to give money found in the mosque to someone whose money has been stolen. The person who finds the money must announce it for a year. If its owner comes forward, it should be given to him. If the year passes and its owner is not identified, then it is permissible for the finder to take it and benefit from it or to give it as charity.