how can I be sure, that the photo from unsplash.com that I would be using (e.g. on my website) isn't actually a picture that was stolen from another person. How can I be sure that the person that the picture got stolen from, is not going to sue me?

Pithy answer, but nonetheless true: you can't be sure, at all. You roll the dice and you take your chances.

There are several cases of content creators (YouTubers, website designers, etc.) going out of their way to find and pay for original photos, stock footage, theme songs, etc., and wind up later getting sued because the person they paid for supposedly original content used copyrighted material, and were forced to take down their entire body of work.

You simply can't be sure. You can try to do your due diligence, and even pay for the effort, and still not know.

In my opinion (completely not based on legal experience at all), your risks are higher of using "free content" from places like unsplash.com precisely because you aren't paying for the free content. Without the profit incentive that image/content brokers like Getty Images have, the ability of Unsplash.com to ensure and enforce rights-free provenance is diminished.

In short, pay up for more peace of mind, or go free/cheap, and expose yourself to higher risk. It's a common business choice.