All these questions do not have a simple answer, but in Buddhist philosophy we have a few possible ideas of why this might happen.
In Buddhism we basically believe that everyone is the same age, since we are eternal beings, the fact that a person is a child and you are an adult is simple a case of perspective.
We are all simply popping in and out of existence at different intervals, and at different times. Just like the atoms in our bodies, the seasons coming and going and the water that moves through-out the earth, via the precipitation cycle.
Now; the idea that a baby can come in to the world and have bad things happen to them is something that is not easy to grasp or to try to understand.
In my opinion; no one consciously chooses their suffering, but I know from our beliefs as Buddhists, we choose our suffering on a different level, (not the level of the conscious mind/brain) as it sets us on a path. But we are not isolated beings as we are all connected, and every thing that we do and experience effects our families, our communities and ultimately the entire world.
Take that young lad dying in the US from bullying about being gay, it has sparked a HUGE debate and people are sitting up and talking about the issues facing gay people.
I see life very much like a play or a drama, we are all actors on the stage of life, and we step on and off that stage with many different masks.
The stories that we tell and the experiences we live are written in the script of that play, and we are the ones who are writing it, as we go and move forward.
Bad things happen to good people, not because they ask for it, or deserve it, but because they are simply on a path that led them through suffering.
It is like walking a path through a forest, we have to struggle through the thorns to get out the other side, but through that suffering we are stronger, wiser and more connected to the source of all creation. (God, Allah, The Universe etc.)
Deep suffering has caused many human beings to break free from their old ways of being and become great and powerful minds and creators.