I heard a Hadeeth that the Prophet, sallallaahu alayhi wa sallam, said that "A person can escape from stones but not from evil eyes." Is this true? I have this because I have been often ruined by it. My neighbor lady who has an afflicted child looks at my children and very often my children and wife fall sick. Is there any remedy? In my home place there is a superstition that they take raw food item in a bowl and circle it around the head of the person on whom the eye has fallen .What did the Qur'an and Prophet say about it?

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.

The effect of the evil eye is a confirmed truth but it does not affect except with the Will and Decree of Allaah. It does not harm anybody save with the Predestination of Allaah. The Prophet said: "The evil eye is true and if anything could be faster (in having an effect) than the predestination, then the evil eye would have been (that thing)." [Muslim] So you have to protect yourself and your children by reading the Qur'an and saying the designated supplications of the morning and evening, it might be that by doing so, you will be protected from the effect of evil eye. If, however, it is predestined that someone will be affected by an evil eye, then Allaah has permitted the means of treating it. In case you know the person who affected you with an evil eye, then you can ask him to perform a ritual washing then wash yourself with water that had been used by the person who had affected you, and, Allaah willing, you will be cured. The person who had affected you should do the following: He should wash his face, hands, elbows, knees, the end of his feet, and the inside of his lower garment in a vessel. Then he should pour the water over you.

Indeed the Prophet said in the continuation of the abovementioned narration: "And if you were asked to perform ritual washing for the person who is affected, then perform it." However, it should be noted that a person should not accuse a Muslim of affecting him with an evil eye without evidence. Basically, a Muslim is innocent until the contrary is proven. If it is not known who affected a person with an evil eye, then it can be treated by Ruqyah, and that is to read verses from the Qur'an and say prophetic supplications, like reading  chapter Al-Faatihah, verses: 255, 285 and 286 from chapter Al-Baqarah (the Cow) and chapters: 112, 113 and 114 and other chapters or verses. As regards what has been stated in the question as placing food around the person who is affected by the evil eye, we do not know any evidence about it, and this matter is closer to superstition than to the truth. Also, we are not aware of any evidence of the narration stated in the question. However, it is confirmed in the narration that we previously stated that the evil eye is true. Its danger is stated in the narration of the Prophet who said: "The evil eye kills (makes the person enter the grave) and makes the camel enter a pot, (i.e. has an amazing effect)."  

Allaah knows best.