Which hour coincides with the last third of the night?

This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.

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.

Does the clipping of nails nullify ablution?

No, it does not, and it is preferable to wash the hands afterwards.

Is it permissible for one to shake hands with his uncle`s daughter?

No, it isn`t because he is a non-Mahram (Marriageable) to her.