well the overspray is probably due to the pressure you are spraying at... I usually spray at anywhere from about 18psi down to 8 or so... (I use a siphon feed airbrush, if yours is a gravity feed you could probably go down to 6 or maybe a little less for fine lines) example: for close in detail work I am sitting about 5psi maybe a hair more... with the brush about 1/2 to 3/4 inch out from the model... again if you have a gravity feed you can go in closer at a lower pressure for finer lines...
the splatter effect is probably from paint not being thinned enough, I *believe* Tamiya recommends a 3:2 mix for some of their paints... you might try that and see if it helps the spattering... the brush also might need a good cleaning, take out the needle and look at it... look for dried paint etc.. remove the head and soak it in the appropriate thinner for awhile and then use a micro brush or Qtip to work the paint out if you find some there..
you can buy a regulator at a hardware store for about 15 to 20 dollars and it will make airbrushing a while lot more enjoyable!!! if money is not an issue for only a slight bit more (30 dollars or so) you can get one from an online hobby source that is graduated in smaller increments and will do the job as well...
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also take the needle and roll it on a flat surface... if the tip of the needle looks like it is wobbling then it is bent, if it is not bad you can run your fingernail along the needle to the tip while you slowly roll it and maybe straighten it, but it is probably worth the 5 dollars or so to buy a new one...