Your friend has recommended a 50 mm f/1.8 lense because it is a fast glass, that means you can have a much wider max aperture i.e. the hole inside the lense that let's the light in. By shooting with f/5.6 you are closing this hole and not using the advantages of a fast lense over a slow zoom.
As you say you were shooting with f/5,6 and 1/15 sec. The speed here is nowhere near enough. Even if everyone keeps still, there will be some camera shake. But when you start opening the aperture, the shutter speed that you can use for this light condition increases dramatically.
At f/4 it doubles to 1/30. At f/2.8 it doubles again to 1/60. At f/2 it more than doubles to 1/125 which is an OK speed. But if you want to eliminate any traces of blur with this kind of pictures, you need at least 1/250 (your aperture needs to be f/1.4) or, better, 1/500 for tack sharp images.
You pay here with a narrower DoF , but it depends on the distance from your camera to the objects.
As you see, there is very often simply not enough light indoors, it often borders on a sufficient amount of light even for a fast lense. It depends on how many windows you have, how large are the windows, if there is enough direct sunlight coming through, time of day etc. if your object is near the window there is suddenly more light, and often it gives you nice shadows.
Bear in mind that we perceive the luminance or the amount of available light very, very differently compared to a camera sensor. We have learned to adapt to light changes through evolution and automatically correct it so it seems not as dramatic as it really is. A sensor in this respect has a linear vision if I may say so. If the amount of light is twice as much it is exactly twice as much for the sensor. For a human eye, or rather brain, the difference is very small, often we do not even notice it.
That is why beginners often were at a loss in the film era when they had to expose manually. These days "manual" mode is not really manual, because cameras have a built-in exponometer, which shows us if out manual settings are correct. Nevertheless even these days you need to learn to "see" the light the way your camera sees it. It will help you to evaluate a scene instantly, choose the right spot etc.
If it borders on a decent shutter speed, use continuos mode, there is a chance that out of 5-6 burst shots one or two will be sharper than others. You can also use a tripod that will eliminate camera shake or simply put your camera on a flat surface. You can also use some fill flash.
One more advice - if you shoot in your living room often,get a white or gray card ( Google it) and use it for your custom white balance settings for your indoor lights and for the mixed light. Save these settings in your camera, it will give you much more natural colours. In the images that you have posted the WB is probably set to Auto, so the colours are way too warm. That is because an incandescent bulb emits a very warm "red" light. Change your WB setting to incandescent and you will see the difference immediately. But white/gray card will give you an even better white balance.