Learn Finnish: Tuo on osasto, jonka projekti alkaa huomenna. - That is the department whose project begins tomorrow.

jonka is the genitive (possessive) form of the relative pronoun joka. Just like a regular noun in the genitive case, it shows ownership. Here, it means the project belongs to the department, so it translates to 'whose' in English. It is in the singular form because it refers back to the singular noun osasto.

Does jonka always come right before the thing that is owned?

Yes. Exactly like 'whose project' in English, the genitive pronoun jonka comes immediately before the noun it possesses, which is projekti in this sentence.

Why does the sentence start with tuo instead of se for 'that'?

tuo is used when you are pointing out a specific thing you can see that is physically a bit further away from you, like pointing at a building or office. se is more often used for abstract things, or things you were just talking about that are not physically present.

What is the -nna ending on the word huomenna (tomorrow)?

This is a fixed time expression using the essive case ending -na. You have seen this ending on days of the week to say when something happens, like maanantaina (on Monday). For the word tomorrow, it is always the set form huomenna.