Can I append the whole compositing network with outputs from other file?

Support Basics & Interface
1

in a simple manner? Maybe copy/pasting it somehow?

2

You can append it from another file. You have to group all the nodes you want to move to the other file first.

Then in you new file:
File → Append → open the source file → NodeTree → Select your Group

3

Thanks Lumpengnom it works