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.

Is it permissible for a woman who is in her confinement to fast upon seeing blood signs that are neither black, nor red ?

Brownish, reddish, and yellowish discharges are all considered confinement until there is no colored discharge which marks the end of confinement. Moreover, the aforesaid woman is prohibited from fasting until she attains ritual purity.

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.

If the Prophet (PBUH) was an Arab citizen in 2009, born in an Arab country ruled by an Arab ruler, saw what was happening to Gaza, what would he (PBUH) have done?