Is it permissible for a wife to give her money to her family as a charity, or a gift without asking her husband, or seeking his consent?

The wife has the right to give her money as a charity, or a gift to her family, or to other people after consulting her husband out of respect, and this is the meaning of treating on footing of kindness and equity. Therefore, if he wanted to stop her from helping her family, then there is no harm in not telling him.

Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?

The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).

Is it permissible to fish on Saturday?

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. 

It is permissible for Muslims to fish on any day, but the sons of Israel are the ones forbidden to fish on Saturday. Moreover, there is no evidence in Islamic Sharia prohibiting Muslims from fishing on that day. And Allah Knows Best.

Is it permissible to offer prayer at home, or should it be offered in the mosque?

All perfect praise be to Allah, The Lord of The Worlds.                                                                                                                                                                      It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.