First shot: for spontaneous, as-they-happen shots you're not going to be able to "set up" and you'll be limited to flash on the camera. If it's pointed right at the subject, you get shadows. No way to avoid them. That's why you turn it to the side and light up the wall, or turn it upward and light up the ceiling. That's "bouncing" the flash. Comes with its own issues, though. If the wall is too far away, maybe you don't get enough light, or the light's color will be affected by non-white walls or ceiling, giving the image a color cast.
Second picture, focus was either never achieved, or lost because the subject moved. If you hold the half-press of the shutter button and your focus is not continuous, it never changes from the first hit until you release the button and start over.
Third picture, slow shutter. Happens if you shoot Av and the light is too low. The camera will use whatever shutter gets the correct amount of light onto the sensor, and it doesn't care what happens during that shutter. Av mode is for control of depth of field, as you set the aperture you want and let the camera figure out the shutter. If your priority is actually controlling motion blur, then shoot Tv, shutter-priority.
Keep in mind, also, that even when using a flash, the camera will try to expose as best it can without considering the flash. In other words, if you're shooting Av and the correct shutter speed that's metered is 1/10 second, It will shoot at 1/10 second. The flash will fill the image but the ambient light collected during that 1/10 is also there, probably with significant motion blur. Consider full manual control when shooting flash photography, set both shutter and aperture to what you want, and let the TTL flash handle the exposure.