Is paying street beggars with the intention of gaining their prayers and seeking blessing through the remembrance of Allah considered permissible and rewarded, or is it forbidden due to the doubt regarding the beggar's need?

It is permissible to give to a beggar unless his lie becomes evident. If his lie becomes evident, then it is not permissible to give to him. If there is doubt about his situation, the 기본 principle is to accept his claim of poverty. There is no harm in giving to a beggar for the sake of his supplication (du'a), because it is permissible to give for a worldly purpose. The intention of charity and enriching can be added to that.