Learn Finnish: Terve! Oletko sinä väsynyt?

In Finnish, you turn a statement into a yes-or-no question by adding the question particle -ko (or -kö) to the main word. Since olet means "you are", changing it to oletko turns it into "are you?".

Is it necessary to include the word sinä in this sentence?

No, it is optional! Because the verb olet already specifically means "you are", the pronoun is already built into the verb itself. You can simply say Oletko väsynyt?. Including sinä just adds a little bit of emphasis to the "you".

I thought the word terve meant "healthy". Why is it used here?

You are correct! Terve literally means "healthy". Using it as a greeting is an old tradition, similar to wishing someone good health. Today, it is just a very common and casual way to say "hello" or "hey".

Why does väsynyt end in -nyt?

The word väsynyt (tired) actually comes from a verb that means "to get tired". The -nyt ending turns that action into a describing word (an adjective) for a single person. For a beginner, it is easiest to just memorize väsynyt as a standard adjective meaning "tired".