Learn Finnish: Maahanmuuttajan kotoutuminen riippuu kielitaidosta. - An immigrant's integration depends on language skill.

This sentence shows the basic rule: the verb riippua (to depend) requires the elative case (-sta/-stä), seen here in kielitaidosta. If you wanted to replace the noun with a whole clause, like 'depends on whether they know the language', you need a pronoun bridge to hold that -sta ending. You would use siitä (the elative of se): kotoutuminen riippuu siitä, osaako....

How is the word maahanmuuttaja formed? It looks like there is a grammar ending in the middle of it.

You are right! It is a compound word made of maahan (into the country/land) and muuttaja (mover). Maahan is the illative case of maa. Finnish sometimes keeps these case endings inside compound words. Here, the whole word is in the genitive case (maahanmuuttajan) to mean 'the immigrant's'.

Where does the word kotoutuminen (integration) come from?

It is built from the noun koti (home). That becomes the verb kotoutua (to make oneself at home / to integrate). By adding the -minen ending, it turns into a noun, similar to the '-ing' or '-tion' endings in English.

Why can't I just translate 'depends on' using a case that means 'on', like the adessive (-lla/-llä)?