What DNS servers am I using?

Here's how I do it:

( nmcli dev list || nmcli dev show ) 2>/dev/null | grep DNS

This worked previous to the way above:

nm-tool | grep DNS

On Debian, you need to have the network-manager package installed.

You should be able to get some reasonable information in:

$ cat /etc/resolv.conf 

On systems running systemd use:

systemd-resolve --status