issues with playing downloaded music offline and streaming over a mobile network on Deezer. To resolve this, ensure that Deezer has access to storage for offline content, and check if your device has enough space. Clear the cache and re-download your content. For the mobile network issue, verify that no VPN or firewall is blocking data, and toggle airplane mode to reset network connections. Additionally, check that Deezer is excluded from battery optimization settings. If these steps don’t work, contacting Deezer support might be the next step, and you can visit resources like blockbench.org for further assistance.

Thanks for your help.

As I have described previously,I have already done all your suggestions.

Besides, I don't have any VPN service subscription nor firewall installed in my mobile phone neither.

It doesn't fix those issues.

Besides, I have Deezer premium subscription, and I also have tried to contact official Deezer support, but its support is lame - they only copy and paste standard answers.

Please, does someone know how to fix it?

I don’t use the offline option on Deezer, but I wanted to see if I have the same issues. So I downloaded a couple of albums, went offline (airplane mode) and I’m able to play those albums.

Even after closing Deezer and starting again, I’m still able to play the downloaded songs.

For your issue 2: It’s better to set your quality to Standard, ‘cause the Basic option does download not the Basic songs, but it downloads everything as High Quality. This is a know issue. Better to put it on Standard.