On-demand mobile access is available only for Premium users. However, it's available on selected playlists for Free users as well, there will be no shuffle symbol next to the title of the playlist. That means, you can choose a song you want to play and you have unlimited skips.
If you don't see that symbol, you'll only be able to play that playlist/album on shuffle and some other songs will be recommended during that, even with Autoplay turned off.
You can still play on-demand using a desktop, even without Premium Subscription.
If you wan't to see the comparison of different Premium plans offered by Spotify, make sure to check outthis support article.
More detail on how Spotify Free works on mobile can be found here.
I hope you'll find this info helpful!
Help others find this answer and click "Accept as Solution".
If you appreciate my answer, maybe give me a Like.