A few questions about the dark knight?

READ CAREFULLY!!! 1st of all, racheal was a hostage for the joker so the cops wouldnt give him much trouble. the joker needed someone 2 lure batman in so he could kill him. also he wanted 2 kill harvey so he could replace his position in being district attorney so he could unmask batman. i know that the joker wanted 2 kill them both so that batman would be in a situation whr he could only save 1 of them and would be blamed for the death of the other but that didnt work out for the joker. so basically, the joker was gonna take Harvey's place, racheal was just a hostage that would get killed, joker would win and batman/Bruce would get blamed for all those killings and letting the joker go.