Learn Farsi: ماده‌ی مربوطه درباره‌ی خاتمه‌ی قرارداد است. - The relevant article is about the termination of the contract.

The ـه at the end of مربوطه acts as a reference marker (anaphoric). While مربوط simply means "relevant", adding the suffix makes مربوطه mean "the relevant one" or "the relevant thing in question". It belongs to the same family of formal reference words as مذکور (mazkur) and نام‌برده (nâm-borde), pointing back to a subject you are already discussing.

I originally learned ماده (mâdde) as "material" or "substance". Why does it mean "article" here?

While ماده does mean "material" or "matter" in everyday or scientific contexts, it has a specific secondary meaning in formal, legal, and administrative language. In those contexts, it is the standard word for an "article" or "clause" of a law, treaty, or contract (قرارداد).

Is خاتمه (khâtame) entirely interchangeable with پایان (pâyân) for "end"?

They share the same core meaning, but they belong to different registers. خاتمه is an Arabic loanword that is highly formal, legal, and administrative—making it the natural choice for the "termination" of a contract. پایان is your everyday, standard Persian word for "end".

Why do ماده, درباره, and خاتمه all take an explicit ی for their ezâfe connections (ماده‌ی, درباره‌ی, )?