Shutter release is like it is in slo motion even at high shutter speed settings.

Are you using flash? Is the red-eye reduction turned on?

Also try setting the camera's menu back to default settings.

Are your pictures properly exposed and are they sharp or are your pictures degraded? Is that 1/3-second you describe a delay between the time you push the shutter release and the time the picture is taken or somthing else? Check to make sure you're in the proper shutter release mode (slider switch to right of the mode dial). Also, your self-timer may be turned on. Your camera allows you to set a 2 or 10 second delay from the menus. If it is set to 2 seconds and turned on, it might seem like a 1/3-second delay. If that doesn't help, you camera is covered by Nikon's warranty. Contact Nikon Service at 1-800-NIKON-US (1-800-645-6687) 9AM-8PM EST, Monday to Friday.

It depends on the effect you want.

• To freeze motion, you need either a fast shutter speed, or a fast flash in a dark environment. In less than bright light you may not be able to get a fast enough shutter speed to stop the action. Increasing the camera's sensitivity to light by increasing the ISO will help some.
  
• You can blur the motion by using a slower shutter speed and a stable camera. Set a slow shutter speed and put the camera on a tripod or other stable surface, and you can get things like streaking car taillights and star trails. How slow a shutter speed depends on the speed of the subject.
• You can pan with the subject. Move the camera with the subject, and keep it moving even while the display blanks out while taking the picture. This will keep the subject sharper while blurring the background to lend a sense of motion to the picture.
• It's either to freeze motion if the subject is moving straight toward or away from you than if it's moving across your field of vision.

Sports mode gives you a high shutter speed. Continuous just allows the camera to keep taking pictures as long as you hold the shutter button and keep the autofocus moving.
You need very high Iso capabilities (6400+) and very fast lenses (f1.8, f2.0, f2.8) to shoot indoor sports and night games under lights and stop motion without a very powerful flash system. Standard consumer stuff just can't do it and even with a good flash it cannot work very far.
You can set the camera to night mode and it will give you your highest iso and slow shutter speeds but you will end up with motion blur.
I shoot a D300($1600) and a 70-200mm F2.8($1900) and I can just barely get away with it. To do it right cost about $8000! I'm now professionally shooting just to pay for the next camera. Hobby too Hell in a hurry.

Image stabilizer (IS) will help you stabilize your shaky hand when photographing static object in dim light environment. When photographing moving things such as humans, camera IS will not and cannot not freeze them unless you use high shutter speed. If your camera allows high ISO and manual shutter speed setting, experiment indoors with it. Just remember, high shutter speed freezes motion and IS can only steady your shaky hand for so long. Tripod can only steady your camera not the subject if the subject is a human being.

In full manual, yes it should.

Your're probably using a flash with TTL disabled. So 1/200 is the highest sync possible with that kind of flash. Did you try removing the flash off the body and setting faster shutter speeds?

If the lighting is low and shutter speed is set for a long period of time its the function of the camera taking the picture. If it is a malfunction of the shutter take it in for cleaning you might have foriegn material stuck in your shutter mechanism

Almost any new digital camcorder will work great, but you want to make sure it has a high speed shutter setting.  Set the shutter speed as high as possible (which means you'll need a lot of light... day light is perfect).  You're still only shooting 30 frames per second, but each shot will be sharper (less motion blur) as the shutter speed increase.  High-end cameras can go up to as much as 1/10000th of a second, but even 1/500 would be great.  Standard, default shutter speed is 1/60th.
For playback, you can use the same camera with a remote control.  Just press play, then just before the swing press pause.  Then use the frame advance button to move 1 frame at a time.  Multiple presses of the frame button will increase the speed... to slow motion.  

Good luck!

If you check out a review site such as www.steves digi cams. com or even the Canon site to check out the spec of the camera to discover what shutter speeds are available. When shooting fast moving subjects try panning the camera on the object as you press the release this will[to a degree] keep the primary image sharp[ish] whilst blurring the background