All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
The father is obliged to spend on his daughter who is not married and who does not have any money. If she has no father, then there are many details with respect to the mother and whether she is obliged to spend on her daughter in this case; the same applies to the brother and relatives in general; whether or not they are obliged to spend on her.
If the father needs care and service, then all his children, males and females, are obliged to do that by themselves or by hiring someone to do this service instead of them.
Al-Khaadimi from the Hanafi School of jurisprudence said in Bareaqah Mahmoodiyyah, while speaking about the rights of parents, “If the parents need service, then their children must serve them.”
Also, Ghithaa’ Al-Albaab authored by As-Saffaareeni reads, “It is their (parents’) rights that their children serve them if both of them or one of them needs service.”
If the father dies and the mother is alive, then it is an obligation to serve her in the same way as with the father.
However, the daughter is not obliged to serve her brothers, even if she is not married. The scholars of Fiqh spoke about serving the parents, and not the siblings or other relatives.
Finally, we do not know what is meant by what you read on that website, that men are responsible to do all these things for a woman in Islam.
Allah knows best.