I need some help on trains. I'm p andlanning to go from Paris to Dusseldorf and Koln, roundtrip. What rail/train am I supposed to take?
From Paris to Koln you need to take a Thalys express train - book at www.thalys.com. You can get significant discounts if you book in advance, but that will tie you to a specific train which may be a problem if you are flying into Paris the same day and the train gets delayed. There are frequent S-Bahn local trains from Koln to Duesseldorf which take about 30 minutes - I don't know if the Thalys ticket will include that.
It will take a bit longer, but you can go via Frankfurt Hbf and use a Europa-Spezial ticket (€39 if you book enough in advance) and any connecting legs (Frankfurt to Düsseldorf) will be included on the ticket. I also saw a Smoovie ticket (Thalys) available on the Bahn website for €29, and I think it included a regional train to Düsseldorf, but that combination might not be available from Thalys.