I guess I'm a looser too. I can't afford a dSLR, so I have been shooting an S700 since last Christmas.
Do not just leave your ISO setting at 64. You can get good results through ISO 200 and OK results at ISO 400. ISO 800 and above is horrible.
For ISO 64, you need a LOT of light. The S700 takes great photos at ISO 64 outside in good sunlight. When the cloud cover comes in, ISO 64 will give you too slow of a shutter speed for a good shot. I select 64 or 100 when I'm outside, and will use 200 with a lot of cloud cover or in shadowy areas such as underneath my trees.
Bright sun, ISO 100, 1/640 s, f/6.8, max focal length (380 equiv.)
Hockey rink very poor light, ISO 400, 1/160 s, f/3.5
Center ice shot from the very far corner 5 rows from the top across from the goal line. White balance edit (see, you can change white balance in a jpeg...), crop, and sharpening. One of my first attempts at more than program mode.
My house is very dark for this camera, ISO 400, 1/60 s, f/3.5, flash -2/3.
I have found with my Fuji S700/5700 that I have to set exposure compensation (EV) down -2/3 for a good exposure. Or, I set in manual for -2/3 exposure.
A good trick I learned with the S700 outdoors in bright sun is, I mostly use manual mode and set the exposure by metering the sky or metering the palm of my hand. In your first photo of this thread, the sun position harms the photo because your son was being backlit by the sun. If you were facing the other direction, you would have the sunlight on your son and have an easier time for your camera to meter the light.
Just to give an idea of where I shot the center ice photo from. This is from the same seat at my widest angle...
Sorry the image is larger than I usually like posting in forums. Bad photo too, I had made adjustments to my settings after this image. It is just here for comparison purposes...
It can take great images of the moon too....
cheap Walmart tripod, ISO 100, 1/1000 s, f/3.5, very very very heavy crop.