I am starting a second post to continue because the previous became too long. The photos look good from tripod but some can not be repeated properly handheld because of the long exposure time.
Here's your first problem. At f8 in low light conditions, your ISO would have to be up in the higher regions of your camera's capability. If you capped it at 6400, then it may not have enough headroom to take a properly exposed picture. I would have shot that newspaper at near the lowest aperture possible to increase the shutter speed to a desirable amount. See: Aperture Priority Mode
The other thing that happened, is that the ISO of 1600 (combined with your particular lens, anyway) is quite low for this environment. Add to that, the high f number and it's no wonder it is underexposed. If your camera chose this ISO on it's own, that's the second problem. Take it out of AUTO ISO.
No, your camera is simply making the wrong choices! You're not truly shooting manual until you control that third piece of the exposure triangle. ISO.
I am sorry, maybe because I did not explain my lens details you may think that I am with the kit lens. I am with 18-200 VR DX. I am not aware of the full capabilities of this lens but expected it to be the same or a little better than kit lens.
I have used the auto ISO in the initial test /not in the last photos/ just to see the camera capabilities and get some first impressions. Now in the last photos I am using the Fn button and the dial to set it manually and have disabled Auto mode in the menu.
That third piece of the exposure triangle is causing me headaches.
One more question, why would you be shooting at f8 when there is not enough light?
The ultimate test would be to take a picture in the sunlight, iso 100 and see what the settings would be. Normally, you should get 1/500 @ f-8. If it's very different, then maybe your sensor is defective. This is all I can think of for now.
Hope it helps a little.
I am using F8 because I want prefer wider depth of field. The newspaper photos and the big set of photos is just for illustration of the low speeds. I take photos mostly outdoors.
When there is enought light /I have not had a good opportunity with this camera yet/ I would expect it to perform excellent / it is quite a decent camera for its money and I kind of like the comparatively low noise level that it produces up to ISO 1600 with so many megapixels/ and that is why I am trying to improve low light ISO or to find what is the problem.
Ok, I understand. OP is under the impression that f8 is the sharpest setting for the lens which is why he chose it.
Just as an FYI, the sharpest stop is actually f5.6 or therearound. But I digress.
The point here is, that f8 is absolutely not appropriate for night photography. You'll want to be using lower f stops for lower light conditions as well as a moderate ISO. With that lens, start at your lowest f stop and select and iso of 800, see if that merits you a better image. Don't worry so much about shutter speed when doing night photography, it really doesn't matter too much as long as the other pieces of the exposure triangle are in place.
I will have to research the aperture size additionally, maybe I am missing something with this lens.
I am mostly interested to improve ISO in low light condition /if it is possible/ during daytime when there is not enough light for example foggy weather, rain, cloudy, etc. The photos I am presenting were to show my point about the speed. The thing is that I am thinking that it starts increasing exposure so steep that I have to apply ISO above 3200 which I believe starts introducing more noise. And the thing is that I would like to take handheld photos /sometimes you don't have time to set a tripod, it is not convenient, etc./.