Learn Italian: Questo vetro, dove lo gettiamo? - This glass, where do we throw it?

This is the classic "left dislocation" structure you're practicing! Because we moved the object (questo vetro) to the front of the sentence to emphasize it as the main topic, Italian grammar requires us to repeat it using a matching direct object pronoun. Since vetro is masculine singular, we use lo right before the verb.

In English, we'd probably just ask "Where do we throw this glass?" Can we say Dove gettiamo questo vetro? in Italian too?

Absolutely. Dove gettiamo questo vetro? is perfectly correct and very common. However, moving questo vetro to the front makes it the absolute focus of the conversation. It translates more closely in feeling to, "As for this glass... where do we throw it?"

Does vetro refer to a drinking glass here?

No, vetro specifically refers to the material glass (like a broken window or an empty bottle going into the recycling). If you were talking about a glass you drink out of, you would use the word bicchiere. This sentence is likely someone asking where the glass recycling goes.

Could I use the verb buttare instead of gettare here?