Running the script from GUI has probably not opened a terminal for you to see it's output.
To run python you need a terminal. To open one you could for example just open the start menu and type 'terminal', then open one of the suggested programs.
Once you have your terminal you need to call the program and give it some arguments to run with, in this case python /path/to/my/file/myscript.py should be enough.
If it didn't work it is possible that python is not recognized by the system. In that case try running python3 /path/to/my/file/myscript.py instead.
If that didn't work as well, you might not have installed python yet. You can install it from the GUI App 'Software Manager' or by using the command sudo apt install python. If that didn't work, you might need to update your sources using sudo apt update.
I also tried to open a new terminal, but clicking the icon will just focus on the currently open terminal, which I can't use because it's already in use for logging something else.
Depending on the terminal emulator (the program that you are using to access the terminal and shell) you should be able to open a new tab in the bar on the top of the window under File > New Tab > [any profile] or alternatively by using the shortcut ctrl + shift + t. That way you will have multiple tabs in the same terminal emulator running separately. The default terminal emulator Gnome-Terminal of Linux Mint Cinnamon has this functionality.
You should also be able to always open a new terminal using the shortcut ctrl + alt + t.
In my opinion this is the easiest way to run any python script. If your really want to avoid running them from terminal, an option you have is to add a desktop launcher and configure it with the command you would put into a terminal.
For that, right click on the desktop and click 'Create new launcher here'. A small window should open where you can put in a name to be displayed, a command to be executed, a comment for the launcher, set an icon, and make it launch from terminal. Enable Launch in Terminal and put something like python3 /path/to/my/file/myscript.py into the command field.
When everything is set up create the launcher and click it to execute your script. (This works for any command).
Keep in mind that your terminal will close once the python script is finished. If it closes instantly, your python script finished instantly.
Tl;Dr:
Command: python3 /path/to/my/file/myscript.py,
run this in terminal (if needed open multiple tabs or windows),
or make a desktop-launcher.
This is the first time i have answered a post on Stack Exchange, I hope it was helpful and not too much detailed. If you have any questions, I would be happy to help.
