You can type about:performance in the address bar of firefox. Then you will get a table where there will be pid of each tab of firefox with Resident Set size and Unique Set Size. And below this there will be some lines explaining the performance of each tab (like performing well) and if a tab is not performing well then it will show there and you can close that tab from there using the Close Tab option.
I hope I have understood your question correctly. I assume the icons you are talking of are those of the tabs in the "Task Manager" widget of KDE Plasma's Panel.
It looks like your question has an answer on askubuntu. There, the question mentions Ubuntu and Gnome, but the answer does not make use of any specific feature of a desktop environment or Linux distribution. I tested it on Arch Linux with KDE Plasma 5.14.4, Firefox 63.0.3, X.Org X Server 1.20.3.
It boils down to a couple of edits to your .desktop files:
1) Add the --class option to the Exec key. It is briefly documented on MDN:
--class=WM_CLASS
Set the WM_CLASS resource class of the X11 windows created by the application.
2) Add the StartupWMClass key. It is briefly documented in the Desktop Entry Specification by freedesktop.org:
StartupWMClass
If specified, it is known that the application will map at least one window with the given string as its WM class or WM name hint (see the Startup Notification Protocol Specification for more details).
With these two options, each instance of Firefox is given its own WMCLASS, so that instances are not grouped together in the "Task Manager". The StartupWMClass sets a link between open Firefox windows and the desktop entries that launched them, letting them keep their custom icons.
To provide an example, assuming your two .desktop files as the starting point and omitting the lines that are not relevant here:
[Desktop Entry]
Comment=First Profile
...
Exec=firefox --no-remote -P test1 --class=firstclass %u
...
StartupWMClass=firstclass
[Desktop Entry]
Comment=Second Profile
...
Exec=firefox --no-remote -P test1 --class=secondclass %u
...
StartupWMClass=secondclass
Best Answer
You don't need to mess with about:config for that. Open up the hamburger menu (three horizontal lines) to the right of the URL bar and click on Customize. There's a checkbox at the bottom left labeled "Title Bar" that you can uncheck.
Edit:
In order get Firefox from Debian Unstable while still using the Stable repository for all of your other packages, add the following to your
/etc/apt/sources.list:deb https://deb.debian.org/debian/ unstable main contrib non-freeNext, add the following to
etc/apt/preferences(create the file if it doesn't already exist):Then run
sudo apt update && sudo apt install firefox