Learn Hardcore Russian: Учитель читает текст вслух.

Russian has no articles at all—no equivalents of “a/an” or “the.”
Whether you mean “a teacher” or “the teacher” is understood from context, not from a separate word.

So Учитель can be translated as “a teacher” or “the teacher,” and текст as “a text / the text.”

What is the grammatical role and form of Учитель in this sentence? Why not Учителя?

Учитель is the subject of the sentence: the teacher.
Its form here is nominative singular masculine (the dictionary form).
Учителя can be:
- plural nominative: teachers (Учителя читают текст вслух — The teachers are reading the text aloud), or
- singular genitive: of the teacher (e.g. книга учителя — the teacher’s book).

In Учитель читает текст вслух, you need the subject in the nominative, so Учитель is correct.

Why is there no word for “is” in Учитель читает текст вслух when we say “The teacher is reading the text aloud”?