The problem is that the compose key works fine, but some application doesn't accept some characters from it. E.g. I can paste the character  in Emacs (Compose+8+8), but this won't work in FireFox, Konsole and Kate. But many other characters, e.g.  typed there (in FireFox, Konsole and Kate) with Compose just fine. Also I may insert a problem symbols with a simple copy-paste (from any of two clipboards).So, what could cause it, and how to fix it?Sorry, but I've no even an idea how to research the issue. I found a peoples whose Compose key didn't worked at all in some apps, but in my case it is works, though somehow partially.Setup: the compose key bound to the right Super key in both /etc/default/keyboard and KDE keyboard settings.
Some apps doesn't accept some characters from the Compose key
x11;kde;character encoding;compose key
Thank @Gilles, I finally found the answer. So, the problem was in the different input methods used by a different applications. I am almost didn't programmed with GUI, so it is hard to say more what that could mean, but at least the problem in the different Compose files  the one used by X is in the /usr/share/X11/locale/<your-locale>/Compose and ~/.XCompose (the last isn't present by default, but you may create it for a custom combinations), and the one used by Qt in Well, looks like nobody knows.The solution is to set xim to be used as the default input method by all an applications. The obvious solution would be to set it in the ~/.xsessionrc like export GTK_IM_MODULE=ximexport XMODIFIERS=@im=ximexport QT_IM_MODULE=ximBut for unknown reasons it just breaks the Compose key for those applications that worked wrong. To do it right you have to call the im-config, and choose there xim as the default input method.