I love #3 as far as colors, lighting, and capturing the moment in the subject's facial expression. I think a lot of my gravitation toward that image is that it has the least amount of sky in it, which on that day appears to have been pretty uninteresting. That is what makes the colors pop so well. I also find that pose / capture to be the most interesting one of your subject.
I also like #1, which comes as a close second for me. Again, I feel you captured the moment and really like the backlit hair and the colors. The warmth suits this shot very well.
#2 looks good techincally, but the pose and facial expression look uncomfortable to me. I don't do portraits myself, so I am no expert; however I take photos of my kids all the time and routinely discard ones where their facial expression doesn't do them any justice. They are also a lot younger, oldest is 2, so it's more of a matter of 'chase and shoot' 
#4 looks underexposed as you suspected, and a different angle might have been more suitable, also closer to the subject would have been my preference.
#5 is a decent shot but I wish instead of the harsh light on the hair, it would have the golden backlight effect of #1; although I understand that is not easily controllable 
I really like #s 6, 7, and 8, in that order, but #3 still wins for me.
Great set overall and I don't think your concerns about warmth are a big deal, I think it fits perfectly.
Oh and last thing, with 8 photos it might be helpful to just number them above each one for people to reference when responding. I kept going back up and counting down to make sure I got the numbers correctly.