Learn Croatian: Otvori prozor, molim te. - Open the window, please.

Otvori is the imperative (command) form of the verb otvoriti (to open). For many verbs, the singular command ends in -i. Because it doesn't have a -te at the end, we know it is directed at one person you would address informally with ti (you).

How would I say this to a group of people, or to someone I address formally?

You would use the plural/formal command form, which usually adds -te to the singular form. So, otvori becomes otvorite. You would also need to change the word for "you" in "please" from te to vas, making the full formal or plural sentence: Otvorite prozor, molim vas.

Why doesn't the word prozor (window) change its ending here since it is the direct object?

You are right that direct objects take the accusative case! However, prozor is a masculine "inanimate" noun (a non-living thing). In Croatian, masculine nouns that are not alive look exactly the same in the accusative case as they do in their basic dictionary form.

Why is "please" translated as two words, molim te?

In Croatian, the polite word "please" is actually a short sentence meaning "I ask you" or "I pray you". Molim means "I ask" and te is the short form of "you". This is why the phrase changes depending on who you are talking to!