Learn Farsi: هیچ کفشی تمیز نیست.

The -ی is the indefinite marker, which usually means 'a' or 'an'. In Farsi, when you use هیچ (meaning 'no' or 'any') before a singular noun, you must attach this indefinite -ی to the end of the noun. So, هیچ کفشی works together to mean 'no shoe' or 'not any shoe'.

Why is the verb نیست (is not) negative when the English translation says 'is'?

English puts the negative idea on the noun ('No shoe IS clean'). Farsi does it differently: whenever you use هیچ (any/no) to describe a noun, the sentence's verb must be negative. So Farsi literally says 'Any shoe clean is not'.

Does adding -ی change how کفش is pronounced?

Yes. The word for shoe is کفش (kafsh). When you add the indefinite marker -ی, it becomes کفشی (kafshi). The emphasis of the word also shifts to that final 'i' sound.

Can I leave out هیچ and just say کفشی تمیز نیست?

Yes, you can. Without هیچ, the sentence کفشی تمیز نیست just means 'A shoe isn't clean'. Adding هیچ at the beginning is a way to strongly emphasize that absolutely zero shoes are clean.