If you are looking for cheap travel between Cologne and Düsseldorf, Flix train is a good option, from cologne hbf to Düsseldorf hbf it costs around 3-4 euros, otherwise db would cost 11 euros (it includes taking bus or a tram or u bahn till your stop). Bla bla is also a good option since some people commute for work daily between these cities.
https://play.google.com/store/apps/details?id=de.hafas.android.db
As suggested by others, the best app to look for connections also you can buy tickets. It has day passes, week passes too.
>https://play.google.com/store/apps/details?id=taxi.android.client
Thanks! There seems to be so many different taxi apps out there, I never know if they're legit or if they even have drivers signed up.
Although this is in English, I know of some natives who go to the events. http://rhinebuzz.blogspot.de/
Another possible option: https://www.xing.com/communities/groups/neu-in-duesseldorf-1069041