Learn Italian: Signore, può portare il bagaglio nella stanza? - Sir, can you bring the luggage into the room?

Because the speaker is addressing someone respectfully as Signore (Sir), they must use the formal Lei form. Può is the form of potere (can/to be able to) for he, she, and the formal you. Puoi is only used for the informal tu.

Why doesn't the verb portare change its ending to match the subject?

Because it follows the modal verb potere (which is conjugated here as può). In Italian, when a modal verb expresses ability or permission, the main action verb that comes immediately after it always stays in its dictionary form (the infinitive). That is why we use portare and not a conjugated form.

Why is it Signore here and not Signor?

You use Signore when addressing a man on its own, just like saying "Sir" in English. If you were adding his last name right after it, you would drop the final "e" and say something like Signor Rossi.

Where does the word nella come from?

Nella is a combined word made from the preposition in (in/into) and the feminine singular article la (the). We need the feminine singular form because the word for room (stanza) is feminine and singular.