Photograph Exposed: Low Light and Fast Action

Shooting indoor and moving object is most challenging situations for me. Only way to take indoor shots successfully is to have more light. How do I get more light on to the sensor?

Left: ISO 80 - Exposure 1/3 Sec - Aperture f/3.5 - Focal Length 6 mm
Right: ISO 1600 Exposure 1/10 Sec - Aperture f/2.8 - Focal Length 6 mm
Perplexed why these images are dark or blurry:

Left: ISO 800 - Exposure 1/8 Sec - Aperture f/5 - Focal Length 6 mm
Right: ISO 80 - Exposure 1/25 Sec - Aperture f/2.8 - Focal Length 6 mm
That is because the lens in my Canon Powershot SX100 IS is not fast due to its minimal f-stop capability. Wish I can replace it with a faster lens, but, it's not an option with what I have. Flash is like a torch--only works well if you are close to the action--and I do not like using it. Only alternative is to manually increase setting such as faster shutter, smaller F stop number, increasing the ISO.

Left: ISO 800 - Exposure 1/4 Sec - Aperture f/2.8 - Focal Length 6 mm
Right: ISO 800 - Exposure 1/8 Sec - Aperture f/5 - Focal Length 6 mm
Below: ISO 800 - Exposure 1/25 Sec - Aperture f/2.8 - Focal Length 6 mm

While shooting indoors, low f-stop numbers let in more light which increase shutter speed capabilities. This one is very grainy

ISO 1600 - Exposure 1/10 Sec - Aperture f/2.8 - Focal Length: 6 mm
...yet interesting and I do like the non-posing composition.

Increasing the f-number (decreasing the aperture diameter) increases the Depth of Field (DOF - deep focus; decreasing f-number decreases DOF (shallow focus). I will explore more on this setting latter in the week.

Here is a string of Continuous play: