Learn Portuguese (Portugal): O rapaz fala com o professor.

Fala comes from the regular verb falar (to speak). Because the subject is o rapaz (the boy), we use the "he/she/it" form (third-person singular). For regular "-ar" verbs, you drop the "-ar" ending and add "-a", giving us fala.

Do com and o combine into one word like de and o do?

No, unlike de + o (which makes do) or em + o (which makes no), the word com (with) stays separate from the article o (the). You simply write and say com o professor.

Does professor mean a university professor or a school teacher?

In Portuguese, professor is used for teachers at all levels, from primary school all the way up to university. If the teacher were female, the word would change to a professora.

What is the female equivalent of o rapaz?

The female equivalent is a rapariga (the girl). Notice that if the sentence were about a girl, the verb fala would stay exactly the same, because "he", "she", and "it" all share the same verb form!