Learn Finnish: Minä toivon, että sinä olet onnellinen.

In Finnish, you must put a comma before the conjunction että (that) when it connects a main clause to a subordinate clause. This is a strict punctuation rule, unlike in English where we usually leave the comma out.

Is it okay to drop the pronouns minä and sinä here?

Yes, absolutely! Because the verb endings (-n in toivon and -t in olet) already make it clear who is doing the action, you can simply say Toivon, että olet onnellinen. Keeping the pronouns just makes the sentence a bit more emphatic or formal.

Could I use haluan (I want) instead of toivon (I hope)?

You could grammatically say Minä haluan, että sinä olet onnellinen, but toivon is usually a better fit here. Haluta (to want) can sometimes sound a bit demanding, whereas toivoa expresses a warm, sincere wish for someone else's happiness.

Why is onnellinen in its basic dictionary form?

Onnellinen describes the subject of its clause, sinä (you). Because sinä refers to a single person and is in the basic nominative form, the adjective describing it must also be in the singular nominative form.