Hi, and welcome!
You encountered, all at once, many of the limitations of a point-and-shoot camera. Let's go through it, with some advice.
First, when the light is low, the camera will have to open up its aperture to get more photons in. And a larger aperture reduces the Depth of Field (or Depth of focus, if you will). That's probably why some parts of the image are blurred, if they were not in the "focus range". That effect is even more dramatic if you use the zoom.
The grainy effect you saw in low light was probably caused by an increase of the ISO value (I'm guessing you had the ISO on auto). When the light source are dimmer, the camera can try to compensate by increasing the "volume" on its detector (the "film"). That means you can expose for a shorter duration, but noise level (grain) will increase.
Some images were blurred because of the low light levels too, I'm guessing. When the camera has no other options, it will keep the shutter open longer to get sufficient light in. That in turn increases the risk of blur caused either by you (no one has perfectly steady hands
) or the people in the frame simply moving around. To avoid blur, the basic rule is to shoot at a speed of 1/60 seconds or faster.
About the windows, to expose properly the inside of your room, you will have to accept that the windows will be completely white. Play with the exposure until your real subject looks good.
About flashes... The S60 has a limited flash power, of course, but there is one thing you COULD do (it can become expensive, though). There are some powerful external flashes that can be triggered by the inboard flash of any camera. So if you could lay hands on such a flash, you could use it with your S60 (those flashes are called "slaves") You could aim that flash at the ceiling, so the light hitting your scene wouldn't be too harsh.
The best camera for your shooting situation would be a digital SLR, because they have larger sensors and thus can use very high ISO values without noise issues to speak of. But they're quite expensive.
Ask away if you have more questions! I hope I helped.
