Question: I thought that the chip they stole was fake? Why did Walter think it is real? Hypnosis?
Answer: It is revealed later on that Allen Scott-Frank, the man from the Macau Science Center, where they stole the fake chip from, was working with The Eye. He likely anticipated their arrival due to being in contact with The Eye and planted a fake chip into the system, allowing the Horsemen to steal it. This fake chip was likely designed to trick a scanner into thinking it was real.
They stole the real chip but lost it. That's how they were able to recognize the one they currently had was fake.
Question: How does Jack hypnotise Merritt's twin brother when he is suppose to be doing a street show?
Answer: The entire sequence in London was all a montage. It is never really established if all of the scenes that took place there were coinciding with each other. The scene where Jack hypnotises Chase could have easily taken place after he had finished the street show.
Answer: Also, the reason why Jack was told to leave early was because when the fbi found out jack was performing, they sent their crew. So Jack finished first, got to the location by the time the third performance was still running, the third performance ended faster than the second performance, the second performance was ended by either Merritt or Jack's "he is hypnotized" call.
Question: While the chip that Walter recovered from the Horsemen was presumably fake (as the Horsemen discovered earlier in the film), why then did they alert the FBI to that chip?
Answer: The only ones who knew the chip was fake were the Horsemen, no one else did. Walter did not know the chip was fake. The plan was to convince Walter that the chip was real so that they could lure him out of hiding with Walter attempting to kidnap and later kill them, and expose Walter to the public in doing so. They told the crowd after exposing Walter about the chip, because while it was a fake, they still had plans with it assuming it was real. If by "alert the FBI", you were referring to when Dylan gave the FBI director the evidence on Walter and Tressler, that was not the chip he gave to her, that was a hard drive containing all of Walter and Tressler's past dealings.
Answer: Walter thought the chip was real because he placed it under a scanner and the scanner confirmed that the chip was real. However, given the fact that later on it was revealed that the whole plane sequence was a set up, it is probable that the device used to scan the chip was actually a fake that was used to make Walter believe the chip was real, most likely throw him off guard.
Casual Person