Question: When David tells Betty of what happened to Bruce as a child, David said that he wanted to cure Bruce but was stopped. If his original plan was to cure Bruce, then why does he suddenly want to absorb all the gamma energy out of Bruce and then kill him?
Answer: He wasn't trying to kill him, he was using his son as a guinea pig. Experimenting on him, poking and prodding him, altering his genetic structure. That trying to cure him was all crap.
Then why try to kill Bruce when he was a child?
Corrected entry: After The Hulk kills the poodle he transforms back to Bruce. The Hulk was naked, which means that Bruce will be naked, but when Bruce is approaching Betty's car a flesh colored covering is visible, used to protect Eric Bana's modesty.
Correction: The Hulk wasn't naked. He was wearing the tattered remains of underwear to cover his modesty.
The entry is correct. You can see the Hulk's bare behind as he walks towards the pond, and then Banner's bare behind after he reverts and walks towards Betty's car, and the piece of clothing he is wearing to preserve his modesty is visible as he collapses to his knees. It's also worth mentioning that any tattered remains of underwear the Hulk would have been wearing would have been far too baggy to stay around Banner's waist.
Question: Why does Hulk agree to give David his power near the end of the movie?
Answer: Because he knew it would overwhelm him.
Well to be honest, I have no clue why David wanted the Hulk power so badly instead of being satisfied with the being he's become at the end of the movie. The guy can turn into anything he wants.
Because he always wanted more. He is a greedy character. Even though he was that powerful, he felt Hulk was more powerful than him, and he wanted that power.
Answer: It's called lying. He was an egotistical mad scientist, who was paranoid and obsessed with proving his work valid. He was willing to do anything to achieve his goals.
David wasn't exactly lying. He attempted to kill Bruce when he was still a child but ended up killing Edith instead when she tried to stop him. General Ross was even there when David was taken away so there is some truth to what David said to Betty.