In the limit, the mixture of Gaussians is a Gaussian.
Nope. The sum of Gaussian random variables is a Gaussian random variable, but a mixture Gaussian model is a very different thing. (In particular, mixture Gaussians are useful for modeling because their components are easy to deal with, but if you have infinite mixtures you can faithfully represent an arbitrary distribution.)
Theoretically, malnourishment (given that only a part of the population suffers from it) should lead to a negatively skewed distribution.
Nope. The sum of Gaussian random variables is a Gaussian random variable, but a mixture Gaussian model is a very different thing. (In particular, mixture Gaussians are useful for modeling because their components are easy to deal with, but if you have infinite mixtures you can faithfully represent an arbitrary distribution.)
Yep, I should have mentioned that also.
Yes, you are correct, I got confused between a sum and a mixture.