Question

I looked around on “the Internet” but could not find a proper answer:

Is there a Google Closure Compiler plugin for Notepad++ or a way to get it working with NppExec.Execute (F6-key).

Answer 1

go and grab http://closure-compiler.googlecode.com/files/compiler-latest.zip, then unzip it.
launch

java -jar compiler.jar --js $(FULL_CURRENT_PATH) \
    --compilation_level ADVANCED_OPTIMIZATIONS \
    --js_output_file $(CURRENT_DIRECTORY)\$(NAME_PART)-compiled.js

which creates a new file which is named as the currently used one but has -compiled.js at its end.