not eat anything/eat nothing

[color=indigo]1) I don’t want to eat anything.
[color=red]2) I want to eat nothing.
Is there a difference between the meanings of ‘1’ and ‘2’?
Are they both natural?
[color=indigo]
3) I don’t want to eat anything for two days.
[color=red]4) I want to eat nothing for two days.
Is there a difference between the meanings of ‘3’ and ‘4’?
Are they both natural?

Gratefully,
Navi.

To me, 1 and 3 are more natural, and the difference is the emphasis lying with 2 and 4.