Is the son obligated to give money to his well-off father who requests it to build his second house, given that the son is in need of money and lives in rented accommodation? And would this money be considered a gift or a loan?

You are not obligated to give your father the money he asks for if he is well-off and you are in need of the money, and this is the opinion of the majority of scholars. A father may take from his son's wealth as he wishes and own it, whether he is in need of it or not, provided that he does not harm the son or take what the son needs, and that he does not take it to give it to another. Abu Hanifa, Malik, and Al-Shafi'i said: A father may not take from his son's wealth except what he needs. However, it is preferable to give the father some money as a gift or a loan if it does not cause you harm, because the father's right is great and showing him righteousness and kindness is among the best acts of obedience.