Thanks for your help!

Yes, I see the spots in the viewfinder in exactly the same way as they appear on the final photograph.

I blew onto the lens from the outside thinking that it could maybe remove the dust on the inside. Don't know whether that's a good thing to do... It had the effect of condensed water inside on the lense, which resulted in a blurry picture. This condensed water luckily disappeared again after a few minutes. The spots slightly changed their position but they were still there.

So, it looks like I have to live with those spots and have to remove them by post editing.