Do I need to collect my checked bags at Bangkok when flying to/from Melbourne?

No, you don't need to collect your checked bags in Bangkok. Your bags are tagged at check-in for your whole journey, whether you fly from Helsinki to Melbourne or from Melbourne to Helsinki.

When you leave the aircraft during the stop in Bangkok, take only your carry-on baggage with you. Finnair takes care of your checked bags, and you collect them at your final destination.