How does a girl draw closer to Allah and behave during distress and when seeking to fulfill needs after regretting a forbidden relationship and causing problems for her maid?

You have done well by repenting. You must strive to honor and treat your parents kindly, for Allah is Most Forgiving: "And indeed, I am Forgiving to him who repents, believes, and does righteousness, and then is guided." If you were remiss in your duty towards the maid, then apologize to her. If your action caused her dismissal, inform your father so that her reputation may be cleared. Do not inform them of the details of what transpired between you and the young man; a sinner should conceal their own sins. For those in distress, there are supplications established in the Sunnah, and for supplications seeking fulfillment of needs, please refer to the mentioned fatwas. Closeness to Allah is achieved by striving for obedience and avoiding disobedience.