The general rule is that you have to take a route given by the journey planner (without entering a via station). Any other routes are considered detours and are not allowed. (See the definition of Travel Route in the terms and conditions.)

In your first example, if you schedule a journey from Amsterdam Central to Leeuwarden/Groningen, you will never get a travel advice from the journey planner that goes via Rotterdam Central. Therefore, you are not allowed to be in a train from Rotterdam to Leeuwarden/Groningen if you have checked in in Amsterdam Central. You don't have a valid ticket in that train and risk a fine.

The same applies for a single trip ticket to Zwolle: the journey planner doesn't give options from Amsterdam Central to Zwolle via Rotterdam Central. In this case, you risk a fine even in the train from Amsterdam Central to Rotterdam Central.

As for your questions about Amsterdam via The Hague to Eindhoven: I'm not an expert when it comes to the trains in that region, but here too the question is what the journey planner would advise you. Since there's no option given from Amsterdam to Eindhoven via The Hague, that's clearly not allowed, but I think Delft would be okay. Breda and further don't seem to be, according to my quick glance at the journey planner.

The text about your direction of travel being beyond your control is about unscheduled disruptions. For example, the regular route from Amsterdam to Eindhoven goes via Utrecht, but if that route is not available, a detour via Rotterdam would be okay. The journey planner would then indicate that route too.

Again, with a single trip ticket from Amsterdam Central to Amsterdam South you're only allowed to take trains that show up in the journey planner. The journey planner certainly doesn’t include options via The Hague or Eindhoven, so clearly you're not allowed to take that massive detour and, again, risk a fine.

The best solution to all of this is to travel with an OV-chipcard and check out and in again at the station where you deviate from the advice given by the travel planner, e.g. going from Amsterdam to Leeuwarden/Groningen you check out and in again in Rotterdam, and going from Amsterdam Central to Amsterdam South via The Hague and Eindhoven you check out and in again in The Hague and Eindhoven. If your check in is within 35 minutes after checking out, then NS will see this as a continuation of your trip and the 200 tariff units cap still applies.

The easiest thing you can do is to not use your OV-chipcard but buy a eticket Day Ticket. With an eticket you can not check in or out, you just open gates with it when you enter of leave a station with gates and you can do all the things you describe without ever checking in of out. 

A day ticket costs twice as much compared to what you’d pay if you kept joining individual trips to one journey. Of course, you can only do this in a window of six hours after checking in for the first time.

Does it? I'm surprised to find they seem to cost inly €58,80 nowadays.

The price of a day ticket is twice the maximum fare of a single trip. If you keep joining short trips together by checking out and then in again within 35 minutes, then the fare will never be higher than the maximum fare of a single trip. As long as the total duration of the journey does not exceed six hours, that is.

Thanks for your kind answer. 

So in general if you use the OV chipkaart and check into the detouring station, then NS will see your detour as a continuation.

Then on the Eindhoven case, since both trains from Tilburg or to Den Bosch run on Boxtel-Eindhoven part, if you checked out at Eindhoven is the trip still considered continuation? or since there’s a repeated part of the journey, it’s invalid to continue and then considered a new journey?

It doesn't matter what the route is you're travelling. You could even be going back and forth between the same two stations multiple times. All that matters is that there's less than 35 minutes between checking out and checking in again, and that the entire journey takes place within six hours.

Discovered something interesting: if you enter stations further than Akkrum, Hoogeveen, Dalfsen and Heino to Asd RAI, you encounter the reisplanner to recommend you to IC to AmZuid and retour back from there, even mentioning “avoid extra cost: transfer via station hall”. From any other station you do not get this recommendation, and the reisplanner tell you to take a metro instead.

Now it’s a pretty legal Travel Route by definition, but how good is the chance if you do get checked by the conductor within that 1 minute of travelling and get fined because nobody understand it’s legal? Forgive me for this is a pretty stupid question and tbh i never ever saw a conductor on that sprinter XD

It's perfectly legal to travel that way; I expect the conductor won't give you any difficulties, but if one does, you can simply show the travel advice in the travel planner to make clear that what you're doing is allowed.

There are other known situations in which this occurs; from Utrecht to Abcoude can go via Amsterdam Bijlmer ArenA, for example. That specific route will cost you extra, though, since you can't avoid the gates at Amsterdam Bijlmer ArenA.

Also note that you can disable Metro in the travel options to see only trains in your travel advice.