What is the ruling on determining the sex of the baby whether through killing the female spermatozoa, or any other way in order to have a male?

If it is done through having a certain type of food, taking a certain type of medication, or organizing the time of the marital relation, then it is permissible.

My husband told me that he concluded our marriage with a fake name that belongs to another person, because he was sentenced. Nowadays, he recieved an ID, passport and birth certificate with the his current name. What is the ruling on being married to him?

Praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.  As regards being married to the person mentioned in your question: The marriage is valid so long as he was the same person your guardian concluded the marriage with, even if he changed his name i.e. if your marriage contract was concluded with the same person, since what counts regarding marriage is the persons not names. And Allah Knows Best.

Is wearing a cap permissible for boys, or girls?

All Perfect Praise is due to Allah, The Lord of The Worlds.

In principle, anything is permissible sol long as there is no Sharia evidence prohibiting it, thus wearing the cap by boys is permissible as long as it isn`t done in imitation of the disbelievers. Moreover, a Muslim woman should avoid all that which attracts the attention of men because whatever leads to the forbidden is forbidden. And Allah Knows Best.

 have an amount of 2,700 Jordanian dinars, which I have invested in a project, and I pay zakat on it every year. However, I have debts and obligations, and this project yields only a profit of about 2-4%. My salary is not enough to support myself and my family to the extent that I cannot pay the electricity bills. Is it permissible for me to take from the above Zakat?