Is a wife considered sinful if she asked for divorce because her husband married another woman?

A second marriage is lawful, and so it is impermissible for you to ask for divorce because of that. If you are certain that you won`t be able to deliver Allah`s rights and those of your husband`s , then it is permissible for you to ask for Khul`a (Divorce on the demand of the wife). However, you should exercise patience since after difficulties, there is easiness by the will of Allah.

Am I permitted to perform more than a prayer within single ablution?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

You are permitted to pray as many as you could within one ablution and to recite Quran so long as your ablution isn't nullified. And Allah Knows Best.

Is it permissible for a wife to boycott (not to attend to his different needs) her husband?

It isn`t permissible for the woman to boycott her husband unless he is the reason behind that, and it is recommended that both spouses seek the advice of righteous people to make reconciliation.

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.