Learn Polish: Zostawiłem klucz w recepcji. Czy mógłby pan go przynieść? - I left the key at the reception. Could you bring it?

This sentence uses the formal pan (sir/you). In Polish, when you address someone formally with pan or pani, you must use the 3rd person form of the verb. So, instead of the informal 2nd person mógłbyś (could you), we use the 3rd person conditional mógłby to match pan.

I thought go meant 'him'. Why is it used for 'it' (the key)?

You are right that go means 'him', but in Polish, pronouns match the grammatical gender of the noun they replace. Because klucz (key) is a masculine noun, you must use the masculine pronoun go in the accusative case (as the direct object), even though it translates to 'it' in English.

Why does the word recepcja change to recepcji?

We are saying 'at' or 'in' the reception, which uses the preposition w. This preposition requires the locative case for locations. Feminine nouns that end in -cja (like recepcja) change to -cji in the locative case.

Does Zostawiłem tell us whether a man or a woman is speaking?

Yes, the -łem ending tells us the speaker is male. If a woman were speaking, she would say Zostawiłam.