I have a free account on spotify, so no premium. But I'm a bit confused because on my mobile phone I can't choose which song I want to listen to and can only skip a certain number of songs, as it is without spotify Premium. But I can do that on my Playstation and my laptop. Is it because I have only just registered there or why is that? I'm a little confused
It's just because Spotify did it that way
That's because you want to listen to more music on the go than at home. And thus can't turn on the desired song on the mobile phone.
It depends on which "interface" you use Spotify. This is possible via a normal browser / PC, but this is even more limited when using mobile devices. As a rule, such services are more likely to be used on the go.
Those are stupid restrictions that can be fixed with the premium version. But it's also free if you have Android: https://apkmody.io/apps/spotify-premium-apk/download/2