I had the same problem with the icon, and then I found well-maintained repositories for Ubuntu (including kubuntu, lubuntu, etc.) 12.04 - 16.04 14.04 – 18.04 at opensuse. So I followed the instructions to completely de-install Pale Moon, then I added the repository and re-installed with apt-get. For my release of Ubuntu:
sudo sh -c "echo 'deb http://download.opensuse.org/repositories/home:/stevenpusser/xUbuntu_14.04/ /' >> /etc/apt/sources.list.d/palemoon.list"
sudo apt-get update
sudo apt-get install palemoon
Just replace 14.04
with the appropriate release number. (Note that it's a little 'x' with a capital 'U' because it it doesn't mean 'xubuntu'; the 'x' is a like a wildcard, so it means any Ubuntu.) Also add the key (with appropriate release number):
sudo wget http://download.opensuse.org/repositories/home:stevenpusser/xUbuntu_14.04/Release.key
sudo apt-key add - < Release.key
Voila! The icon appears correctly in the launcher, and it is installed no longer in /opt
but in the way other Ubuntu applications are, and easily updated besides.