Question: How did the League of Shadows use economics to attack Gotham?
Answer: They used their influence to trigger the economic depression that was gripping Gotham when Bruce was a child.
What type of influence did they have?
It's never specified in the film, so any answer would be pure speculation. They merely say they attacked Gotham economically in the past. I'd presume they'd use power and threats to do things like tank companies, make people lose their jobs, increase homelessness, make it more difficult for people to get help, etc. Basically, just ruin the citizens financially.
Question: I was wondering about the final scene between Ghul and Batman. Batman says he doesn't have to save him and lets him fall in the train and the microwave generator explode. Despite this film being closer to the comics than the previous films, isn't this still against the "code" Batman adheres to in the comics? This was one of the reasons Bruce Wayne has to stop Jean-Paul Valley's new Batman in the Knightfall/Knightsend series. (Valley had let someone die).
Answer: In the Knightfall series, Valley chose to go after a bad guy instead of go to the assistance of an innocent. In Batman's view of things, that is a lot different (and a lot worse) than simply chosing not to rescue a bad guy from a train about to crash.
Question: What happened to the Scarecrow? Rachel just tasers him and he rides of into the shadows seemingly still alive?
Answer: At the end of the movie, when Gordon and Batman are on the roof Gordon says, "The Narrows is gone and we still haven't rounded up Crane or half the inmates of Arkham."
Answer: Exactly. The filmmakers set it up so that he can reappear in a sequel. Comic book villains (in more recent movies, at least) are very rarely killed, they somehow always survive to possibly come back later on. Crane appears in The Dark Knight rises.
Answer: He appears at the beginning of "Dark Knight" as a common drug dealer.
Question: Shouldn't Bruce be as insane as Falcone? Unless the dosages delivered to Batman and Falcone, respectively, were different. Also, why didn't Rachel yell and scream and go crazy like Falcone did when he was hit?
Answer: Bruce is just as infected as Falcone, however he is rescued by Alfred shortly after he is poisoned and given an antidote by Lucius shortly after that. He is then bedridden for many hours. If he had not been saved as quickly as he was, he no doubt would have been a blubbering mass just like Falcone. The reason Rachel and even Bruce don't react the same as Falcone the moment they are poisoned comes down to how each individual person reacts to fear: Bruce tries to fight, Rachel faints, Falcone screams in horror.
Answer: Also he had taken it before, earlier in the mountains.
Answer: Bruce was thoroughly trained to deal with fear. It's likely he'd be able to hold his mind together better than most.
Answer: By having their own people working inside the trading company, they would do a pump and dump. Take a small company, put the word out that it's the next big thing, watch the prices rise, then sell. Like insider trading, the millionaires become billionaires, while the billionaires become broke.