Hi 5taras, and welcome to the forums. First off, you should not try and mix using the nightly from the AppImage and the one from the ppa repository - the repository uses the milestone 1.0 version, which is out of date and can't run TFTD.
Secondly, on first running the AppImage it doesn't detect any installations because it doesn't know where to search for the data - by default, it will create a folder at ~/.local/share/openxcom, and this is where you need to place a folder called "TFTD" containing all the files from the original game. So, first you should purge the openxcom from the PPA from your system, then look for the ~/.local/share/openxcom folder, and make a TFTD folder there containing GEODATA, GEOGRAPH, MAPS, etc. - all the data from the original game.