Is it permissible for someone who has forgotten to mention the supplication pertaining to answering the call of nature to say it while in the toilet?

It is disliked for a Muslim to mention Allah while in the toilet, but he/she may recall the supplication in his/her head without uttering it; that is in case he/she had forgotten mentioning it before entering the toilet.

Is it permissible for the woman to use her mobile phone while on the street?

All Perfect Praise is due to Allah, The Lord of The Worlds 

Modesty should be observed by the woman at all times, so she is free to use her phone while on the street as long as it is done within the limits of Islamic manners. And Allah The Almigty Knows Best.

Is it permissible for a person who had vowed to give a certain amount of money to another, but didn`t find the latter to donate that money to the mosque?

In principle, the vowing person should abide by his vow as much as possible. Therefore, if he couldn`t find the person that he had made the vow for, then the vow itself is countless and nothing is due on its maker. However, if the latter happens to find the former later on then, he has to give him that money.

What is the ruling on giving Zakah (obligatory charity) to one`s relatives?

It is impermissible to pay Zakah to one`s origins (parents and grandparents) because providing for them is an obligation on their branches (sons and daughters) if they were poor, but it is permissible to give some of the Zakah money to relatives whose provision isn`t due on the giver of the Zakah.