Is it permissible to give the mother 500 EGP from the price of the bedroom set that the maternal uncle is making, knowing that the husband is unaware of this, and the mother needs the money for food and treatment?

If you own the money you will be paying, there is no objection to giving some of it to your mother. However, if the money belongs to your husband and you have been given the right to dispose of it as an agent, then if your uncle reduced the price after the contract for manufacturing the room became binding, this reduction is a permissible gift to you, and you may dispose of it. But if the reduction was before the contract became binding (during the option of the session, or a condition, or before that), you are not permitted to dispose of it, because an agent acts in what is most beneficial for the principal. In this case, you must seek your husband's permission and request his approval after explaining your mother's need and the virtue of charity.