An additional compass I had missed yesterday, was going to add it: Either a North arrow to the North direction (which of course could then point to anywhere near 6 o'clock) or, much better, a direction arrow for North, East, South or West but anywhere in the range of 10 o'clock to 2 o'clock - in practice, you probably will have a compass like in your pic, somewhere to the side, with all four directions, which is not as immediately comprehensive.
It's interesting you say that besides a gps, also a compass has to be integrated into the device. I hadn't thought of this, all the less so since I did some tries with several compasses, including car compasses, and all of them were heavily distorted from the electronics within the instrument panel. Only when I held them far away from that, with my arm behind my back, near the back seats, the showed the North correct again. Since navigation devices are fixed on/near the instrument panel, I wonder how a compass in them could be precise, from these tries.
From your description, I become aware that I did not clearly enough distinguish the different problems. When you are as a tourist in some other country, being online data-wise can quickly become quite onerous, especially if heavy data traffic (mapping) is involved. On the other hand, most navigation devices do not download their maps in real time but have them stored in the device itself and use some web services just for gps, or even get gps positions from some satellite, for free, so they do not need any web communication at all.
I admit I only superficially know navigation systems from some years ago, so I hadn't been aware of their map functionality today, which is different from their route functionality and which had been the only one I knew. So after reading you, I downloaded a manual from Garmin, and from TomTom each, and I found that map functionality, but without a manual turning function for the map and with rather bad or missing compass: No pic for Garmin, rather poor pic for TomTom, in both cases I downloaded manuals for rather expensive devices.
It seems - the descriptions were not precise, so I could be mistaken about this - they both automatically present the map in a way that your current route/street driving direction goes more or less up, not down the screen, but that up also can be just slightly up and decidedly to the right or the left instead, and there does not seem to be any manual way of turning the map, but zoom they have.
All of them function without web access, the maps are bought and downloaded into the device once and for all. The same for asmand.net for Android from your example, and which is free, and there seem to be lots of such apps for Android and also some for iPad.
Garmin/TomTom can be bought as apps, which frees you from the rather tiny screens of navigation devices, more expensive ones will be at risk anyway in the parked car, so it seems reasonable to buy a tablet instead, of 10" size, and to fix it near the steering wheel with some holder, then clip it out when you leave the car, ready to use it in a more general way then - I was going to buy some 7" mini tablet but that would be too tiny for maps in the car since when driving, the least fiddling around with the screen is best, so a bigger screen will be better, needing lesser fiddling.
As for the compass you speak of, I got some interesting info from some Apple help forum where they speak of electronic compasses which are in-built into iPhones, but not into iPads, according to them, and they say iPhone and iPad apps are different and not only different in screen size, as I had thought you could use the same Apple app on both which is not the case then, but, and here it gets interesting, they say some map applications (!) have an in-built electronic compass, which obviously means that an electronic compass is not a real compass which then transfers its data electronically to some app, but it's not a compass at all but just software which checks history of gps data and calculates the direction of the movement of the device from that, so if I'm not mistaken here, the problem with physical compasses will not be relevant anymore.
But if the device doesn't move, there is no recent history of different gps data, so you would need an internal compass, as you say, and you are obviously speaking of a real - magnetic - internal compass - or how would it be done otherwise?
As for google maps which you mention, I always use them on my pc - and I print out screenshots as get-there-maps and destination maps from them which I use in the car, so I'm thankful for red lights - so I don't know of their functionality on the move, but it seems evident from past searches on that matter that google maps need web access for heavy map downloading.
Considering prices only, I should very probably buy a Samsung Galaxy Tab A 10,1 with a robust car holder, since it has got a resolution of 1920x1200 pix and seems to be reasonably fast, and then trial free and paid map software for/on it, iPads start at double the Tab A price, with some 30 p.c. better resolution and probably not being faster at their starting prices.
But an internal compass neither of them have, while the Samsung Tab 3 - but which is old and slow and quite bad, screen resolution a mere 1024x800, has got one, physically it seems, and lots of apps rely on that internal compass, googling "samsung/android tab compass" will bring discussions on problems arising from missing compasses, so, even without really getting why there is a problem, I think a missing compass could become a problem, according to the app, even on the move, so that criterion should probably not be discarded too early.
Anyway, thank you very much for your very helpful info, 4wd, which was new for me: It seems that my problem can be quite easily resolved with the right hardware and the right software, with some tablet and perhaps a paid map app, since to be frank I quite abhor the look of Openstreetmap. Besides, Bing Maps are really beautiful, so I use them more and more on my pc instead of google maps, at least for big, standard towns where they are precise enough, which is not always the case elsewhere.