Learn Portuguese (Portugal): O fato do médico é cinzento.

It is a classic false friend! In European Portuguese, fato means "suit" (like a business suit). If you want to say "fact", you use the word facto (and the C is actually pronounced). Note that if you ever speak to someone from Brazil, they usually say "terno" for suit instead.

Why do we say fato do médico instead of using an apostrophe-s like in English?

Portuguese does not use an apostrophe-s for possession. You must always use the structure "the item of the owner". Here, we combine de (of) and o (the masculine "the") to make the contraction do, so fato do médico literally translates as "the suit of the doctor".

Could I use está instead of é since a person can change clothes?

No, because we are describing the suit itself, and its color is a permanent physical characteristic of the fabric. We use the verb ser (here conjugated as é) for inherent qualities like color, material, and size. You would only use the verb estar for a temporary state, like if the suit is currently dirty (está sujo).

Why does the adjective cinzento end in an O here?