Learn Portuguese (Portugal): Tu lembras-te da nossa professora, não é?

In Portuguese, we don't translate English tag questions like "don't you?", "aren't we?", or "hasn't she?" word-for-word. Instead, for a positive statement like Tu lembras-te... (You remember...), we simply add não é? at the end. It literally means "isn't it?", but it is the standard way to ask for confirmation after a positive sentence.

Could I use pois não? here instead of não é??

No, because pois não? is used to confirm negative statements. Since the main sentence Tu lembras-te da nossa professora is a positive statement, you must use não é? to ask for agreement.

Why is it da nossa professora and not just a nossa professora?

The verb used here is lembrar-se, which means "to remember". In Portuguese, this verb requires the preposition de before the thing or person you are remembering. Here, de combines with the feminine article a (meaning "the") to make the word da.

Why is there a -te attached to the verb in lembras-te?