Is it permissible to secretly take money from one's parents to buy psychological medication? And is that considered unlawful (haram)? And is buying a dog for psychological purposes and raising it in the house unlawful (haram)?

If you are unable to earn a living and have no money, then your maintenance is obligatory upon your father, as is customary, and this includes the cost of any medication you need. There is no harm in taking the cost of the medication without his knowledge, as long as it is an obligatory right upon him, especially if the father would not object to it. Customary permission takes the place of actual permission. As for owning a dog, it is not permissible except for a necessity deemed legitimate by Islamic law, such as guarding or hunting.