What is the ruling on a woman working in writing Gulf series and going to the filming location where there is mixing between men and women, and is the money earned from that unlawful?

Series in general are not free of forbidden things, such as ostentation (tabarruj) and unlawful mixing (ikhtilat), and this includes الخليجية Gulf series. If the act is forbidden, it is not permissible to assist in it, as Allah says: ﴿And do not cooperate in sin and aggression﴾. Writing plays that are forbidden by Sharia falls under assisting in sin, and thus it is not permissible.