I have two questions which I wanted to be answered:
1) Can a person give Zakaat by estimation and by being sure that the Zakaat amount is more than what he acquires?
2) Is there any special prayer due to which Allaah gives a person a power through which he can read other peoples mind? I have heard of few good Muslims who have these powers of course given by Allaah.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

There are evidences which prove that it is permissible to give Zakat by estimation in relation to date-trees or viticulture and other similar fruits. However, some jurists differed in opinion regarding certain fruits. As regards the Zakat for money and other currency that serves in its place, there is no evidence about giving the Zakat by estimation. However, if the person who wants to give the Zakat of his money is sure that he will give more than the amount which will be calculated from his money, then we do not see any harm. Giving Zakat is something good, as Allaah says (which means): {And whoever does good voluntarily, then verily, Allaah is All-Recogniser, All-Knower.}[2:158]. However, one has to make the intention that whatever is in surplus of the Zakat is a charity.

As regards your question about supplications by which Allaah gives power to a person to read people's minds, we do not know any supplication in the Qur'an or the Sunnah in this regard. No one can know what is in a person's mind but Allaah. Concerning what you have mentioned about some pious people who have such powers, then this is an insight that Allaah puts in the hearts of whom He wills of His slaves. Thereupon, they know the conditions of some people, either by miracles, insight, inspiration, or presumption. They look to the situations of people with the insight of their hearts. Allaah says (which means): {Surely! In this are signs for those who see (or understand or learn the lessons from the Signs of Allaah.}[15:75]. Ibn 'Abbaas interpreted the verse to mean: "…for those who have an insight". Of course, it is only a heart that is purified from all kinds of impurities and disobediences, and which seeks nearness to Allaah that sees with His Light as it is He Who puts it in the person's heart at the first place. There is also another kind of insight which is acquired through experience and evidence, and this insight could be acquired by Muslims and non-Muslims alike.  

Allaah knows best.