I would use AF-C and 3D tracking on whatever player you want to photograph next, giving the camera a bit of a moment to find focus, then do a couple shots with continous hoping to catch a good frame. Thats about the only tip I can tell you for your current setup, without changing hardware.
Well, Sport/Action is simply the hardest category of photography when it comes to demands on the camera. A D5100 is not really that much up for such a challenge. ISO 1400 is my personal limit with that camera for "clean", noise free shots, and you are already stepping beyond that. Raising the ISO even higher is not much of an option, because over ISO 6400 the camera starts to have really ugly colors as well. Thats when you really love a full frame camera like the D600, because they allow you ISO 6400 with no problem and even ISO 25600 is definitely still possible.
And you seem to use the cheap AF-S 70-200 f4-5.6 VR DX zoom that I own as well. Again, this isnt much of a lens for sports - relatively slow autofocus and all. My new AF-S 70-200mm f4 VR has a lot more punch when it comes to AF, but it was expensive.
You still have it good though. Its kids sport and you dont really need much range, and you have the 1.5 multiplication factor to effective focal length thanks to using an APS-C sized sensor (which Nikon fancies to call "DX"). You could get a fast and relatively (compared to other focal lengths) cheap 50 f/1.4 lens and gain 2 stops even over a hefty f/2.8 zoom for around 400 "bucks". Only problem with this is of course - thats again not the fastest autofocus motor in that. And you no longer have the option to zoom.
Picture #1 has the wrong focus. The people in the background are sharp, the players have a general blurriness that suggests out of focus (instead of just a movement blurr that shows a direction).
Picture #2 is definitely out of focus. Again the camera catched the people in the background that are not of interest but are squeaky clean sharp (at least at this low resolution, anyway).
Picture #3 looks okay-ish, except of course the faces of most players are hidden by the net.
Picture #4 seems pretty good. You have movement blurr because of the low shutter speed. You can either love that for the added dynamic look of the picture, or hate it because you wanted to freeze the action.