Most of us here are beginners, and we all have to start somewhere right? I think you did a great job - especially with child photography. Firstly because they are often either really shy or really goofy in front of the camera and they move - and move fast. Hopefully this is okay, but I am just goign to give some CC (constructive critisicm)
Personally, I don't mind the noise at all. With black and white I believe it adds character. Now, that beign said, I agree with Mike, the purple hue is not doing it for me. Perhaps a straight black and white, or slight (very slight) sepia hint would look better?
Try taking a step back, perhaps seeing what the individual is looking at, laughign out, shying away from adds so much more than just their facial expression. For instance in post #2, the expression is very interesting - but I have no idea who are what she is interacting with or reacting to.
Next, the shadows. Try takign a few photos in full shade - it is amazing teh difference, it just smooths things out.
Overall, you did a wonderful job with exposure and focus - you can tell these kids are also rather comfortable with you behind the camera, and that is one of the most important things. I am looking forward to seeing more