Learn Finnish: Minun kuulokkeeni ovat rikki.

When you add a possessive suffix (like -ni for "my") to a word in the basic plural form, the plural marker -t drops out completely. Because of this, kuulokkeeni is spelled exactly the same whether it means "my headphone" or "my headphones".

If kuulokkeeni can mean either one or many headphones, how can we tell it's plural here?

You have to look at the verb! Since the sentence uses the plural verb ovat (are) instead of the singular on (is), we know the subject must be "my headphones".

Where does the double "e" in kuulokkeeni come from? The dictionary word is kuuloke.

Kuuloke is a noun that ends in -e (just like huone or osoite). The rule for these words is that their final -e doubles into -ee- before you attach most endings, including a possessive suffix.

Why isn't rikki (broken) in a plural form to match the headphones?

Rikki is a special "invariant" word. It never changes its shape to match the case or number of the noun it describes. Whether one thing is broken (on rikki) or many things are broken (ovat rikki), it always stays exactly the same.