a couple of things to note:
First, you have a custom path for the icon, so changing the default icon won't make any difference.
Second - we'll probably ignore the other issue(s) you've raised (multiple instances in the dock) -- I recommend you search for solutions to that, and see if you can find an answer, and if not, post it as a separate question.
Back to the headline question -- "how to change the default terminal icon?"
My solution was to give up and use a custom icon. Mostly because I long-ago came to the conclusion that the upgrade churn of Ubuntu wastes too much of my time, so I was better off keeping my customisations safe from the developers. My particular need is slightly different from yours -- for a ROOT terminal with matching icon. So here's my solution.
contents of ~/.gnome/apps/menulibre-root-terminal.desktop
Comment=xfce4-terminal with root privileges
This file has been modified a number of times over the years (most recently to implement pkexec, when the churn killed gksu). It is also for xubuntu, so it is not directly applicable to your situation. But close enough for some guidance. Note the path for my icon for this launcher. I have several that have accumulated over the years. I have attempted to attach a couple of them for you to experiment with. gksu-root-terminal.png utilities-terminal.png
Working from this example, I use find, and discover that the launcher for the default terminal (not the one I am using) on my system is called:
Inside that file I find the Icon= declaration. It says:
doing a find, as below, reveals a plethora of candidates, at which point I would likely be off to the xfce.org website (and probably the xubuntu website) to ask someone there for some help. -- like "which one of these is referred to by the launcher?", and "how does an ordinary mortal know for sure?"
(FWIW, my money would be on the first one, and I would take a flyer and try renaming that file, putting some obviously different image in its place, with the same name, ownership and permissions. But I'll leave that up to you.)
find /usr/share -iname '*utilities-terminal*' -print
NB -- after re-reading and editing all this, I am going to guess that you are not using the term "default icon" to actually mean the default icon for the system, but rather you just want a custom icon for your terminal app. In which case, you just need to put a suitably-dimensioned svg, png, jpg, whatever, image in a known location, then edit the launcher in the GUI to point at the new image file.
note that the utilities-terminal.png is really utilities-terminal.svg, converted using gimp -- stack exchange doesn't accept .svg files for upload.
(the unshifted ~ key).
/usr/share/applications/can you try with
/usr/share/applicationsby the way what is the current icon theme you are using?