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Because there is no connection between yemeyi and bir şey. And such a connection is not possible. But "yiyecek" functions as an adjactive when it is placed before "bir şey" and they have a connection because of this. 

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Yes. 

Ex. yemek is a verb. If I add ecek sufix I make it an adjective. So it becomes an adjective verb. You can use an adjective verb as a noun too. Is it complicated?

and also you do not use accusative case for indefinite objects like "bir şey".

Bir şeyi de yap.

Bir şeyi de bil.

but i think it is just exceptional idiomatic common usage. because you always say:

- Sana bir şey söylücem. (not "bir şeyi")

- Bir şey yapmamız lazım.

But it deserves a more extensive research.

Exceptional or not they are accusative

I do accept that they are accusative. That is why I call them exceptions

"istisnalar kaideyi bozmaz."