Greetings, Tikaram!
Thank you for your answer and for passing the matter on.
The third issue mentioned above was that – when set for the entire site (on Windows) – the Sticky Player will open on another page anew and start playing from the beginning – and will not continue playing without interruption from the previous page (Homepage) – which I’m just guessing was the original intention.
For now, I solved it by setting all new pages to open on a new tab, so the player (now set only for the Homepage) continues playing in the background, which seems to work both on mobile devices and PC – though without immediate control of the player.
Regards,
Gaudelier