What is the validity of the claim that whoever recites Ayatul-Noor 226 times will have their insight illuminated and see things before they happen, and that whoever recites Ayatul-Kursi 313 times will achieve the same?

What your friend said about the virtue of reading specific verses a certain number of times is not based on any Shar'i (Islamic legal) evidence, because such rewards can only be known through revelation. To claim it without evidence is considered a lie against Allah's law and an innovation (bid'ah) in the religion. Allah Almighty says: "Indeed, those who invent a lie against Allah will not succeed. [For them is but] a brief enjoyment, and there will be for them a painful punishment."