This is unfortunately the expected behavior for the camera you purchased. It is an extremely basic model with a very limited ISO range for the sensor and a fairly slow lens for the size. It's really more designed for taking daytime and well lit photos and is basically the equivalent of a cheap camera phone, but with a very basic lens put on it to give it some zoom capability. There simply isn't enough in the budget of such a cheap camera to be able to spend any more than the minimum on each of the components and this means lots of corners have to get cut.

The ISO is the sensitivity to light that the sensor can support. ISO 1600 is not particularly high and that is the maximum listed without going in to high sensitivity mode. This isn't really sufficient to get any kind of decent low light images without having lots of noise in the extended ISO range for the camera, which is non-ideal.

Additionally, the lens speed (or aperture) is limited to 3.1 for the wide angle (zoomed out) and 5.9 on the tight end (zoomed in). This is the widest that the opening to let light can become (smaller lets in more light). It is quite small for the size of the camera lens and sensor size, so it isn't letting in much light to get to the sensor either. You will get more light if you stay near the wide angle (zoomed out) though since the aperture can let in more light.

So overall you have a sensor in the camera that isn't very good at capturing images that are not well lit coupled with a lens that can't let in a lot of light. That combines to give you the low light performance issues you are experiencing and is honestly normal for any camera in that price range. The only real solution with that camera is to shoot in better light if wide angle shots are still getting too much noise.