Never heard of appImage, will have to read a bit.
You can also build Avidemux on Ubuntu/Mint from source easily:
sudo apt-get update && sudo apt-get install git
git clone https://github.com/mean00/avidemux2.git
bash createDebFromSourceUbuntu.bash --prefix=/usr/local
If everything goes well, you should be able to run Avidemux with the command
You must uninstall other Avidemux packages first!
I'm sort of thinking of trying completely different distro far from Mint/Ubuntu like Suse and try to install Avidemux there.
Why? Avidemux can't be the reason, even if you get e.g. 2.6.15 packaged by rpmfusion.org on Fedora.
Also opening the mp3 file I simply open Avidemux, click open, locate the mp3 file and hit open.
This won't work this way. You must load a video, then you can add your mp3 file as an external soundtrack ("Audio" -> "Select Track" -> ".... Add audio track" from the track dropdown menu).