There is absolutely no point in us judging your choice of depth of field, because that is a matter of choice (up to the point where the lens is wide open). The question of what DOF is correct or even appropriate is entirely a matter of your personal taste or objective.
You haven't explained what you mean about the noise. We have no way of knowing whether the noise level in the upper picture was artificially injected as part of post processing or is due to some other cause, such as using a high ISO setting. In other words, we do not know what is the issue with respect to noise - so, what is your point?
Regarding the exposure, I suggest that the dynamic range in the scene is well beyond what you are able to show here, because the highlights on the lower picture are blown out and the shadows are blocked up and have too little detail. The same problem seems to be the case for the upper picture as well but not as extreme. Take a look at the histogram - the highlights are clipped at that end and the shadows are clipped at the other end. It's as if no effort has been made to get the dynamic range within bounds (such as through more diffuse lighting or by filling in the shadows with an auxilliary light source).