Is it permissible for a woman to seek financial support from her father by resorting to the judiciary, given her employment and need, and her father's neglect of her and refusal to marry her off?

A father must provide for his daughter until she marries, unless she has sufficient wealth or income. If your salary is not enough, or if you wish to leave your job due to its hardship or the presence of impermissible شرعية elements, you are permitted to do so, and your father is obligated to provide for you. If he fails to do so, you have the right to sue him.