ALL of this is IN the VRR area-they offer 24 hr daytickets, stufe D (network wide) for slightly less as NRW-but without the AM peak restriction, smaller area thus. Prices go up 1/1/23 anyway.
You CAN do the whole, with luck with trains on time (not garanteed at all) in around 3 hrs-start from Düsseldorf main. In that 24 hr you could hence also ride all (but not the full networks) of the 6 tramway networks, where Essen+Mülheim are now combined as Rurbahn and Oberhausen does not have its own and a trolleybus in Solingen. The trams of Köln+Bonn and Bielefeld are also in NRW, but out of that VRR.
HINT: in that city MANY HTLs offer free travel on VRR -or for a very modest sum (like 2-3€/day) included in their rates-which are pretty low when there is NO Fair=messe going. Same-same for Essen city-but fewer such HTLs. Also ALL DB-associated IC=INterCityHotels offer this, these are also in Duisburg and Dortmund. Personally I do not really like them-but anyones taste. They currently run a special 20%-off promotion, perhaps only for members/those who have subscribed to their offers. A simply google will speedily lead to those HTLs.
That 7,30 is likely the price for 24hr stufe A=1 city only, and hence will not cover any transport out of that city. You would have needed to buy several of these and also tickets for in between=much more as that 30. Even start from DUS, it would have been possible with clever combining on 2 singles stufe D-till/from Dortmund, but I guess even that would cost more as that 30-and MUCH more as the free HTL passes.
