The default player has basic customization options as colors and position, but you can also build any custom player with Elementor:
To create a custom player and replace the default player:
1) Make a new "Mega Footer Header" (tutorial) , and create a custom player in your Mega Footer. Make sure to check it also in responsive view.
2) In the customizer, change the player settings and set it to invisible
3) Go to the Customizer, to Mega Footer or Mega Header, and load your custom player. This will appear in all of the pages.
To make the custom player Sticky, edit the custom player from Elementor, in the Advanced settings > position, and select Fixed positioning, to bottom left, and set its width to the desired size, for instance 100% or 100VW for a full width player bar.
Making a custom radio player with Elementor
https://pro.radio/updates/custom-radio-player-builder-for-elementor/
https://pro.radio/web-radio-tutorials/how-to-make-a-custom-player-in-elementor/
In alternative to the widget Custom player, you can also create the single elements manually using Button, Song Title Feed, Artwork and more, and creating manually the columns to contain your custom elements.
More info:
https://pro.radio/shop/knowledgebase/483/4.24-Radio-Feed-Titles.html
https://pro.radio/shop/knowledgebase/484/25.-Song-artwork.html
https://pro.radio/shop/knowledgebase/35/4.6-Button.html
You can make one player for mobile and one for desktop, using the Reponsivity features of the Elementor sections. So you can set one section to be visible in desktop, and one in mobile, using the Hide/show features of Elementor for the different sections.