Is it permissible to offer Salah (prayer) on behalf of the sick who is on his/her death bed, and is incapable of offering it?
It`s impermissible to offer Salah on behalf of the sick, or the dead.
Is housemaid right hand possession?
All perfect praise be to Allah, The Lord of The Worlds. May His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Housemaid isn`t right hand possession. Rather, she is a free woman because she is just hired to deliver a service. And Allah The Almighty Knows Best.
What is the ruling on Qonot Du`a (supplication) at dawn prayer?
All perfect praise be to Allah,The Lord of The Worlds It is a confirmed Sunnah, and whoever leaves it should perform Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.
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.