Perhaps you'd prefer to just walk around doing good without any control over it, because the solution to most of those questions would involve God controlling everyone. Yes, free will exists, and yes, people will do with it what they feel like. As for the cancer, the five year old is, according to the nearest Mormon, automatically sorted into the highest level of heaven for dying young, and honestly if his wife died a year later the 'why' is looking more like 'it's genetic'.
Thousands of starving children die every day because we haven't moved on to hydroponic farming yet. Most of these have to do with people exercising their free will, directly or indirectly. As a rule, God doesn't interfere with that.