No I don’t use vpn.
The first problem was solved. I just had to disable KDE wallet and in Wi-Fi & Networking => Wi-Fi Security, I entered my wifi password and selected ‘Store password for all users (not encrypted)’ and after reboot the problem was solved, It didn’t ask for password anymore and limited connection was also not shown. I don’t know if that’s how it was solved but I didn’t face the problem again.
As for second problem with Bluetooth and Wi-Fi, like you said it was due to interference of frequency both being same (2.4GHz). Your suggestion for solution on changing the Network Adapter worked for me. I changed my driver from rtw_8821ce to rtl8821ce and wifi is working while I am listening song on my earbuds rn 
Thank you for helping solve this for me 
@Frater_418 and @Olli