Well I don't think Batman's identity would be that hard to deduce, especially for someone like Light. Its beyond me how no one guessed Bruce as Batman over the years. Personally I think Light would figure out Batman's identity faster than Bruce would figure out Light's.
Thats true. Who would have enough money to afford all that crap, look for all the rich people and deduce from there. If that doesnt work kill all rich rich people or hold Gotham ransom.