I would hate to think so. I really have a feeling that it's someone from the former Eastern Bloc who put his services on the market a long time ago when the cold war ended. He probably started out working for the Russian Mafia relatively cheaply and has steadily risen in reputation, capability, and ruthlesness.
The reason why I think he's not a Muslim is because a little while ago one sniper shot and killed a bunch of Israeli soldiers. I don't know if it's the same guy, but if the Muslims were capable of producing a hit man like that, then it stands to reason that there would be dozens of snipers pinning down Israelis every day.
Many military, SWAT team members, and even casual hunters have the capability to make the shot. The defining characteristic is in actually shooting a child. That is the biggest clue to me. Where is there a record of children being shot by a sniper? I can only think of two:Yugoslavia and Chechnya. That's where I would start to look because this man has definitely shot children through a sniper's scope before.
I happen to agree with that. I doubt they would be doing things like this when their style is usually to strap on a bomb and go on a bus. It still is possible that it is a muslim organization that hired this guy, but more then likely just some lone gunman like you suspect.