Is it possible to make POI’s click able? The idea behind is, that I want to click on the next (for example) petrol station and a menu shows up with (Routing to, Routing from, Routing over).
I don’t want to tap + hold on the map and then have to select the point by re-ranging the location.
On the website this feature is already implemented.
No, it is not possible.
They are not overlays to have events, they are inside the map.
No, it is not implemented for OpenStreetMap POI inside the map.
(and you can not compare 2 different platforms)
The custom POI on the website are overlays.
This is the right process for map to get events and select locations accurately.
So does this mean the custom POI in this website is an overlay? (See screenshot)
You can even see the time when the petrol station is open. (This is very nice). And it’s possible to select the POI as start or end of the trip.
I don’t get the meaning behind the manual re-ranging location (for POI’s). I assume that POI’s are not moving, so why not click on the POI and select route to or route from? Is there a technical obstacle? I mean this function would it make easier to start or end and at certain POI’s.
Yup, all those blue items that you see on the map (all those that can be turned on / off in the “marker” menu) are imported from other services or websites 
For a website such things are often quite easy, because you can just make a call to some kind of interface and it gives you the result. In apps you often have to integrate a whole library and get into all kinds of interfacing troubles when somebody doesn’t give you the data you expect 
It can be hard to explain the difference in a non-technical way, so please ask if anything is still unclear!
@Patrick thanks for the detailed answer.
Would it be possible (in the future) to get this for the android app too?
Would be nice if the user could select only the POI’s he would like to see (for example: petrol station, bank, restaurant, hotel)
In theory, yes, but as I said it’s a lot of work and probably far down the priority list for kurviger’s (only one) android developer
This is a work for the future and a different implementation:
