Is it possible using Apple Remote Desktop to connect to computers over the internet (so different networks) ** without ** having to tweak the router settings of those devices?
PS currently using both Mojave and Catalina
Unfortunately, not any more. It used to be possible using Back to my Mac, which was abandoned at Mojave.
See Does Apple Remote Desktop connect to computers over the internet? for how it used to work.
Also ref: Wikipedia - Back to my Mac
Not a total solution but I use Teamviewer now where I used to use ARD. It works without router tweaking and is easy to set up at the remote end.