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.

A woman used contraceptive pills, and her menses exceeded (15) days, is it permissible for her to fast?

The maximum of menstrual blood is (15) days, but if it exceeded that due to a medication, or the like, then it is Istihadah (bleeding outside the monthly period), and in this case she should perform Ghusl (ritual bath), pray, and fast. Moreover, she is obliged to make up for the missed fasting days which exceeded her regular menses. And Allah Knows Best.

Is Zakah due on a woman`s deposited gold?

Zakah (obligatory charity) is due on deposited gold if it reached Nissab (minimum amount liable for Zakah), and a lunar year had lapsed over owning it. The due Zakah is (2.5%). And Allah Knows Best.

Should a person feel pleased, or have a virtuous vision after offering Istikhara (guidance prayer) in order to do what he/she had offered it for?

The result of the Istikhaarah is not necessarily that a person sees something (in his dream), or feels pleased, but the most important result of the Istikhaarah is whether a person is enabled to do a given matter or not.