Does the "tali'" (natal chart) have a slight influence on a person, as a previous fatwa indicated, especially with studies on the influence of moonlight and its gravitational pull on living beings and human mood?

The lunar mansions (Tawali') are not causes, and there is no evidence to support them being causes; rather, the evidence indicates the opposite. The optical effect of the moon or the tides during lunar days is not proof for determining the merits of a person born at those times, and this cannot be used as a basis for knowing the future or judging a specific characteristic.