As far as I have understood, you have asked two different questions...
...does Allah own the events like children dying in a bomb as well?...
To understand answer to this question, you have to understand two different and fundamental aspects of Islam.
Death is not end of life. This life exists for limited duration.
No; but you prefer the present life, whereas the Hereafter is better and more enduring.
For a person who thinks that this life is the only life, death and pain are the most scary things. They are unable to understand how God can tolerate death of a young child.
And yet, what is death. It is just a return to Allah. Why is it so terrible?
For a person who refuses to think of anything beyond this life, this life is unjust! Many big criminals who indulged in mass murders lead prosperous life. Many humble people who dedicate themselves to service of society face terrible ends.
I am not saying that death of child in bomb blast is good or desirable. I don't know how to say this. For a believer death of someone close is sad. Yet it is different from what an atheist would feel. For believers death is not the end.
A second aspect of this answer is, everything in this world (and next) is in complete control of Allah.
To Allah belongs the dominion of the heavens and the earth and all that is in them and He has full power over everything.
Nothing can happen without Allah allowing it to happen. However Allah has given limited freewill to humanity for a limited time.
Allah allows us to take decisions. This leads to many evils that you see in the world. However when Allah allows these evils, it does not mean that Allah supports it. It just means that Allah chooses not to punish the criminals immediately.
In some cases Allah tests people through alteration of good times and calamities.
We will surely put you to trial by involving you in fear and hunger and by causing loss of property, life and earnings. And give good tidings to those who remain steadfast in these trials: when a misfortune comes to them, they say, "We are Allah's and we shall certainly return to Him", Their Lord will bestow great blessings and mercy upon them; such are the people who are rightly guided.
The second question you have asked is...
Then there are people who say that Allah wants you to do something about it etc.
Who says that? Your responsibilities are related to your abilities.
Allah does not burden any human being with a responsibility heavier than he can bear...
You don't have to go anywhere. You have responsibilities where you live. You can spend money in helping poor and old people in your community. Your responsibility might depend on how much money you have! Of course, if you are in position of power, your responsibilities will increase. If you president of your country, you may have obligation towards international peace!
If you feel strongly about what is happening in - for example, Syria, then pray for them. What you pray remains between you and Allah.
..."Our Lord, take us not to task if we forget and lapse into error inadvertently. Lord! lay not on us the kind of burdens that You had lain on the people before us. Lord, lay not on us the kind of burden that we have not the strength to bear. Be kind to us, forgive us and show mercy to us. You are our Protector: help us against the disbelievers."
Note: If you are down-voting my answer, you are most welcome. Please provide reasoning in the comments. I promise, I will not argue with you. I am writing this since unexplained down-votes have perplexed me earlier in this forum.