Any du`a which has not been narrated in a report and which is not part of another act of worship is regarded as general du`a; in this case there is nothing wrong with raising the hands.

Allah doesn’t answer your Du`a: 1. When the Du`a is weak in itself because it involves something inappropriate, or involves bad manners towards Allah. 2. When the one is making Du`a is weak in himself, because he is faint-hearted in his turning towards Allah. 3. When one has done something that Allah has forbidden, such as having prohibited wealth or one has taken a prohibited job, or the stain of sin is still in his heart, or he is following Bid`ah in religion, or his heart has been overtaken by negligence. 4. When one consumes prohibited wealth. 5. When one tries to hasten the response. 6. When one makes the Du`a conditional, such as saying, O Allah, forgive me if You will or O Allah, have mercy upon me if You will.

There are many dua`s that you can say to remove depression, anxiety, grief, and sorrow. Read these du`as in the detailed answer.

There is not, as far as we know, any du’a for finding a good spouse that has been reported from the Prophet (peace and blessings of Allah be upon him), but you can pray to Allah to bless you with a righteous spouse.