At least for the resolution, the problem is one of data rate. While it is easy enough for a camera to rapidly capture a few 12 megapixel images per second, video uses 24 or more frames per second. The sensor and image processing hardware is simply not fast enough to deal with capturing 24 or more full resolution images per second.
Further, even if it was able to capture the higher resolution, there is nothing that can display that high of resolution. 4k screens are only about 8 megapixels in resolution and they are still fairly new (didn't exist at all at the time the D5000 was made). 1080p video would be nice, but that's still only using 2 megapixels of the sensor.
Also, it is not possible to shoot video when not in LiveView. When you are looking through the viewfinder, there is a mirror blocking the path of light reaching the sensor and instead directing it to the optical viewfinder. Since the light isn't reaching the sensor, it isn't possible to record or capture anything. This is why the viewfinder goes blank for an instant when you take a photo, because the mirror has to swing up out of the way.
With LiveView, the sensor is left exposed and the image from the sensor is instead displayed on the screen so that you can see what you are doing.
As for the aperture, shutter and ISO issues, those are limitations of the camera software. It may be possible to overcome them with a third party hack for the camera, but I don't know if one is available for your particular camera model.