Hello! Can you please specify the exact servers where you can reliably reproduce the problem while you query VPN DNS? Note: if you cant' resolve names with other (not AirVPN's) public DNS, then the problem should be related to a broken connection, and not to VPN DNS: @root1337
The error:
VERIFY ERROR: depth=1, error=certificate is not yet valid: implies that the device date is incorrectly set to the past and the certificate is not yet valid in that date. It's possible that the router could not sync through NTP during the bootstrap. Actually the first DNS server you set (10.4.0.1) is accessible only from within the VPN, therefore it will not resolve any name, including NTP server names. The router will then fall back to the second DNS, the OpenNIC one. Since OpenNIC servers have been replaced and some of them suffered downtime, try a different DNS server (for example Quad9, address 9.9.9.9). Anyway this problem seems unrelated to the other DNS issue you report.
Kind regards