In the past I've been able to find the prices for German Rail twin passes (50% more for the second person), but I can't find them anymore. I can only find tables where it's a per person price; two people are twice as much. If you've found a twin price, please show the link, othewise I'm assuming my page has the right prices.
You show 10 venues and 9 ">" marks, which are trips between venues. One trip, I know, Köln to Düsseldorf is a very short trip. I think a local regional train or tram ticket is about 15€ pP. It's in second class, but the whole trip is about 30 minutes. It's probably not worth an ICE ticket or a day of a rail pass. So that leaves 8 trips for a pass.
The German Rail Flexi pass comes in 4 day, 5 day and 7 day versions for 600€, 664€, and 770€ respectively. That works our to 150€ to 96€ per day for two people.
Since you already have your accommodations for the trip, except for Frankfurt to Köln you should be able to count on making the specific trains for each trip, and therefore Saving fare tickets are a viable alternative to a pass.
Frankfurt to Köln is at the end of a trans-Atlantic flight. I don't think you can count on using a train-specific ticket for that leg. You might be able to still get a Rail&Fly ticket "extension" from you airline for that leg, but if not, a day of a rail pass might pay off.
So you should certainly explore Saver Fare tickets for each leg. Go to the Bahn website and look up each leg and see what the 1st class Saver Fare tickets are currently going for. Don't use Super Saver fares. They are totally non-refundable.
Look up on the Bahn website what Saver Fare tickets are available for each leg. It they are less than about 110 euro, buy them. Then see what more expensive legs are left that might justify a rail pass. I doubt that there will be any.
In 1988, I went to Germany for the first time on my own dime for 14 days. I bought a 16 day continuous 2nd class pass for $160. That was a great deal. In 2000 I went back and paid the same, $160, for a pass for, I don't remember, maybe 5 or 6 days. After I came home, I looked up the fares for the trains I used, and I think I just about broke even vs. individual tickets. Since then, I have always analyzed my trips, individual tickets, regional passes, saver fares vs. a rail pass, and I've always found I did better without a pass.