Learn Portuguese (Portugal): Ela fala devagar.

Because it needs to match the subject Ela (She). In the present tense, regular verbs that end in "-ar" drop the "-ar" and add "-a" for "he", "she", and "you" (formal). So, falar (to speak) becomes fala.

I learned that Portuguese adverbs usually end in "-mente". Why is "slowly" translated as devagar?

You are right that many adverbs end in "-mente", and you could actually say lentamente (slowly). However, devagar is a very common word that just naturally means "slowly" without needing a special ending. In spoken, everyday Portuguese, people use devagar much more often than lentamente.

Can I change the word order and say Ela devagar fala?

No, that would sound unnatural. In Portuguese, adverbs that describe how an action is done usually go right after the verb.