Regarding your question, 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 that you want to play and you have unlimited skips.
You can still play on-demand using a desktop, even without Premium Subscription.
Spotify Free can help you find new music. That means you will get suggested tracks for your playlists if they contain less than 15 songs. The more you listen, the better the suggestions will become.
At the moment, it's not possible to disable these features.
However, if this is something you'd like to see in the future, I'd recommend heading to Ideas Exchange and posting it here.
Here is more information on how the Ideas Exchange works.
In addition, here's an article comparing different Subscriptions offered by Spotify. Take a look if you're interested.
I hope it helps!
Emilia_8Rock Star 10
Help others find this answer and click "Accept as Solution".
If you appreciate my answer, maybe give me a Like.