Can I just own a Finnish company from abroad, or do I have to actively work in it?

The permit is not granted for passive ownership or investment alone. You must take an active role in running the company and your main income has to come from that business.

If you are mainly a silent investor or your livelihood comes from another source, this is not the right permit. Be ready to show how your day-to-day work in the company generates the income you rely on.