Is it possible to make kataifi dough (by yourself or starting from filo dough)? I really like the thready structure in this dish. But when I look for recipes, they all ask for a box of kataifi dough. I haven't found this in regular supermarkets (I haven't been to greek stores), so I was thinking if I could make it myself.

Would it be best to buy filo dough (which is thinner than if you would make it yourself) and shred/cut it; or to make filo dough yourself (so you would have longer pieces than store-bought dough) and cut/shred it?

How do you shred it exactly? And how would can you replicate the correct form of kataifi (like a roll)?
I am afraid that it is quite hard to prepare it yourself. And you don't start from phylo dough. 

Kataifi is not shredded, it is spun. You need a hot metal wheel for that. It is made from a batter which is thrown on the wheel, and because the wheel is spun, it bakes on the wheel in threads. You need not only the instruments (this wheel), but also quite a bit of experience to throw it in even threads. Kataifi makers are a popular attraction on middle-eastern markets. If you can't visit one, you have to visit an ethnic grocery store to buy the prepared kataifi noodles.