Learn Croatian: Umorni smo. Stoga idemo ranije kući. - We are tired. Therefore we are going home earlier.

The word kući (the dative case of kuća) is used to show direction or motion towards your house. This perfectly matches the action verb idemo (we are going). If you wanted to say you were already at home (a fixed location), you would use the phrase kod kuće or the adverb doma.

I usually say zato for "therefore." Can I use zato instead of stoga here?

Yes, absolutely! Both mean "therefore" or "for that reason." Zato is very common in everyday casual speech, while stoga is just a little bit more formal and frequently used in writing. They are fully interchangeable in this context.

Is ranije an adjective or an adverb in this sentence?

Here, it functions as an adverb meaning "earlier", modifying the verb idemo (we go). It is the comparative form of the base adverb rano (early). In Croatian, comparative adverbs are very easy to spot because they share the exact same form as the neuter singular comparative adjective.

If the word mi (we) is omitted, how does the adjective umorni agree with the subject?