Does the canon lens 50mm f1.8 have image stabilization (especially in low-light/indoor)?..?

no it does have image stabilization. But its a very fast lens (large aperture) so it does not need is. And yes, you can take shots at high speed at low light with the aperture wide open, but you will still have a lot of noise unless you hav a full frame sensor. But the lens really gives sharp images when stopped down to 2.8 its going to cheap wherever you buy it (its the cheapest lens by canon) but buy it first hand. The build quality is like a toy and a second hand will surely have defects.