Is it permissible for a young Muslim man to help an elderly Muslim woman, who is not a mahram to him, with her household chores such as cleaning and cooking, or to enter her home for the purpose of teaching her matters of her religion?

The Sharia prohibits entering upon non-mahram women. The Messenger of Allah, peace and blessings be upon him, said: "Beware of entering upon women," and "No man should be alone with a woman, nor should she travel except with a mahram." This is because Satan may beautify a woman to a man, and vice versa, which could lead to indecency. It is preferable for women to serve one another. If that is not possible, then it is permissible for a man to serve her, provided there is no seclusion and with lawful controls, such as the presence of a mahram or another woman.