Learn Finnish: Luin kiinnostavan kirjoituksen tänään. - I read an interesting article today.

The root is the verb kirjoittaa (to write). By applying the suffix -us, it becomes the noun kirjoitus (a piece of writing or article). This suffix often creates a noun that is the result of a verb's action. To act as the object of this sentence, the noun's stem changes to kirjoitukse- and takes the -n ending.

Why do both kiinnostavan and kirjoituksen end in -n instead of being in the partitive case?

They are in the accusative case (which looks exactly like the genitive in the singular) because the action is complete. You finished reading the entire article. If you were still in the middle of reading it, you would use the partitive case for an ongoing action: Luin kiinnostavaa kirjoitusta.

Where does the word kiinnostavan come from, and why is it used as an adjective?

It comes from the verb kiinnostaa (to interest). Adding the -va ending turns it into a present active participle, which acts just like an adjective meaning "interesting" (literally "that which interests"). It then takes the -n ending to match the case of the noun it describes.

Could I just use the loanword artikkelin instead of kirjoituksen?