Yes you can have IDE2 and IDE1 both installed on same machine.
Appimage on Ubuntu: Currently has a minor issue that a shared library is not installed by default on Ubuntu.
fixed by: sudo apt install libfuse2
Covered several places including:
https://itsfoss.com/cant-run-appimage-ubuntu/
Arduino is working on update to their appimages to be more contained. Not sure if yet in daily builds or not.

make files are easy? oops I did not update to say filex now depends on filez and it did not rebuild correctly....
Build from Source? - Are you talking about building Arduino? or building your sketch? Yes their build setup to build the actual IDE is pretty complicated.
Building your own sketch, depending on if your files are all in your sketch folder. You click on verify or upload...
IDE2 update 1.8.19 settings? Unclear what you are asking? Note: Teensyduino installed under 1.8.19 does the installs of all of the Teensy stuff
under whatever IDE you are installing over, as Paul needed to update some the underlying things of the IDE.
With 2.x - Teensy install is like most any other board type. And it's files are installed in the standard Arduino boards location. In the Arduino15 location.
So it does not use any of the same files. Obviously if you edit the same sketch using the two different IDEs, it will stay changed for both of them.