What DNS servers are used when connected to wireless data?
While the setprop method to change DNS does not work, the getprop method to read those values should be still valid today:

shell@A0001:/ $ getprop | grep dns
[dhcp.wlan0.dns1]: [192.168.1.1]
[dhcp.wlan0.dns2]: []
[dhcp.wlan0.dns3]: []
[dhcp.wlan0.dns4]: []
[net.change]: [net.rmnet0.dns2]
[net.dns1]: [208.67.222.123]
[net.dns2]: [208.67.220.123]
[net.rmnet0.dns1]: [208.67.222.123]
[net.rmnet0.dns2]: [208.67.220.123]
[net.wlan0.dns1]: [208.67.222.123]
[net.wlan0.dns2]: [208.67.220.123]


To clarify my answer: using a terminal emulator app (like Terminal Emulator for Android), as a normal user (no root permissions needed), you can execute the command I showed (getprop | grep dns) and get an output like that.