Learn Farsi: تو گل را برای معلم می‌آوری.

را (râ) is the definite direct object marker. Because you are bringing a specific flower ("the flower" instead of "a flower"), Farsi requires you to put را immediately after the noun that is receiving the action.

Since را (râ) makes it "the" flower, why isn't there a را after معلم (mo'allem) to mean "the" teacher?

را (râ) is only used for direct objects (the thing being acted upon, which is the flower here). معلم (mo'allem) is not the direct object; it follows the preposition برای (barâye - for). Farsi doesn't have a standalone word for "the", so for words after prepositions, we just rely on context to know it means "the teacher" and not "a teacher".

What do the different parts of the verb می‌آوری (mi-âvari) do?

This verb is made of three pieces. می (mi-) is the prefix for the present tense, showing an ongoing or habitual action. آور (âvar) is the root of the verb meaning "bring". Finally, ی (-i) is the ending that matches the "you" subject, تو (to).

Do I have to include تو (to) at the beginning of the sentence?

No, you can leave it out! Because the verb ends with ی (-i), everyone already knows the subject is "you." Saying گل را برای معلم می‌آوری is a very natural and common way to speak in Farsi.