I have a student NRW ticket so have never had to purchase a ticket. I was quite surprised when I found out that the ticket machines were actually for the Skytrain and not just for those connecting to DB regional trains, however. I always thought it was part of the airport infrastructure, like a free intra-terminal train.

A day pass for the airport viewing terrace is also valid on the Skytrain.
Before these daypasses were cheaper than normal Skytrain tickets iirc

However, you can no longer buy tickets for the viewing terrace at the station since the terrace that was once located there has been closed a few years ago.

This is just to let you know that on my way to the airport tonight I met two young ticket inspectors on the Skytrain, who rigorously controlled everybody's tickets and assured my that the Skytrain was gebührenpflichtig. I told them that I had thought the Skytrain was part of the airport infrastructure, like a shuttle between terminals. I had a VRR Preisstufe B ticket, which is valid on the Skytrain, and I always have this when I go to the airport.

Tip: a bit OT, but in the VRR area of Nordrhein-Westfalen it's worth getting a 10er Ticket which is available for smartphone only. A Preisstufe B 10er Ticket costs EUR44, which (at EUR4.40 a ride) represents quite a saving on the normal single ticket price of EUR5.80. Going to Düsseldorf city would be Preisstufe A, which is a lot cheaper, and you can get a 10 ride ticket for that too. These are valid for one way journeys only, and are valid on the Skytrain in one direction connecting onto/from other train and S-Bahn services.

There is a major construction done between Duisburg and Essen during the Autumn holidays of North Rhine-Westphalia. I was under the impression, the S1 is running a dertour ... but this is incorrect. Information available only in Germany language is here: Verkehrsverbund Rhein-Ruhr - Totalsperrung Duisburg - Essen
You can go back to Derendorf and try to catch the S-Bahn S6.

The RE1 and RE6 should stop in Essen-Altenessen. There you have connection to the Essen local transportation network and can take the subway / underground to downtown Essen. This is better than "Schienenersatzverkehr" between Duisburg and Essen, especially during peak times.

2.5h is just insane. Isn't there usually a direct RE train every 20-30min between the two train stations?

And why would you voluntarily go to Oberhausen in the first place? :p

It is insane and it makes me a bit angry that in many ways Germany is a country that imposes, slightly Soviet style, that you have no choice whatsoever. So you have no choice of an airport bus or other form of transport, just that rubbish VRR system, overpriced by two and a half times what the cost should be. And when the VRR goes down, it goes down. Of course, I could take a taxi, but they are about 50 Euros to Oberhausen. Having said that, yesterday I returned to the airport leaving at stupid o'clock (for a country that pretends to be efficient like Germany) and it deposited me there only 5 minutes late, so I enjoyed breakfast the lounge. And going back to choice, you will NEVERl get a glass of tapwater when you need it in a restaurant or cafe in Germany, EVEN if you buy drinks (don't get me started on this one!).

I suppose one good thing about that daft Preisstufe system in the VRR is that it is also valid on the airport SkyTrain, but that thing should never have a Gebühr, it should be part of the airport infrastructure, like it would be at any normal airport (just trying to pull myself back on topic).

As for Oberhausen, I have my partner there, even though I am away in Switzerland much of the year. The city, like most places in the Ruhrgebiet, has many secret corners if you look a bit deeper. That goes for most of the Ruhrgebiet, as evidenced by the beauty I have found thank to my various hiking books (Rother, Kompass, ADAC, etc.). I think of the Schloss, bridge and canal in Oberhausen, Kettwig by Essen, the Dortmund Zoo area, The Bochum Bermuda Triangle, Mülheim by the Ruhr river, the Duisburg Forest and so on (just to give some ideas).

If you arrive to Dusseldorf by ICE that includes a City-ticket, I would expect this to cover the S-Bahn and the VRR Skytrain. Is that correct ?

It would in mosts cases.

If you however buy a deeply discount Super Sparpreis, this does not include the city option anymore. The regular Sparpreis ticket as well as a fully flexible ticket does include the "City Ticket".

Super Sparpreis does offer you the ability to book a city option, which would be an indicatgion for you, that the "City Ticket" is not included

If you hold, as the poster suggested, an ICE ticket that includes a City-ticket than you will be entitled to use the Skytrain not in "most" but in "any" case without a further ticket. If you hold a ticket - what the post did not suggest - that does not include a city ticket, that you will not be entitled to use the Skytrain without a further ticket. ;)