Is it permissible to say: "O Allah, by the status of the saints and the righteous, and our master Muhammad, peace be upon him, grant us the ability to reach Ramadan"?
What is mentiond by the righteous predecessors that they used to say: "O Allah bless us in Shaba'an and Rajab and give us the ability to reach Ramadan." [Shoa'ab Al-Iman/vol.3/pp.375]. And Allah Knows Best.
Is it incumbent on a family to provide for its old handicapped son and take care of him?
The family and relatives - e.g. brothers - of such a person are obliged to spend on him and take care of him if he didn`t have money of his own.
Does touching women temporarily forbidden in marriage nullify ablution?
It is prohibited to touch, or to shake hands with such women as they are considered strangers, and doing so nullifies ablution.
What is the ruling on having brotherly ties between a strange man and a strange woman, and is the former considered a Mahram (unmarriageable) to the latter?
Such a relation between a strange man and a strange woman is forbidden in Islam because it involves forbidding what Allah has allowed by marriage, and allowing what Allah has forbidden such as looking and the like. Such a relation doesn`t render any act lawful between them, thus they are forbidden to look at each other, have a Khulwah (seclusion), and travel together.