Question: After one of the Imperial officers told Vader that the Millenium Falcon's hyperdrive had been deactivated, and then Luke and the others escaped anyway, why didn't Vader get angry? He killed a couple of officers earlier for losing track of the Falcon.
Answer: Well, he killed *one* officer (Captain Needa) for losing track of the Falcon. But all we can do is speculate... Perhaps it was the final failure, since his plan to turn Luke to the dark side didn't work. Perhaps he had second thoughts after meeting his son face to face. Perhaps Vader was concerned that if he was too aggressive, he might tip his hand that he had tempted Luke by suggesting the murder of the Emperor. Whatever the reason, Admiral Piett seems just as surprised as the audience that he wasn't executed.
Question: I once read something about a chimpanzee being in this movie somewhere. No joke. Has anyone else read or heard this?
Answer: This is likely what you are referring to: When the Emperor first appeared in The Empire Strikes Back, he was portrayed by Marjorie Eaton under heavy makeup. Chimpanzee eyes were superimposed into darkened eye sockets during post-production. Https://en.wikipedia.org/wiki/Palpatine#:~:text=over%20military%20force.-, Portrayal, was%20voiced%20by%20Clive%20Revill.
Question: Before contacting the Emperor, Vader tells Admiral Piett to move the ship out of the asteroid field for the transmission. But if the Emperor was able to contact Piett, why not just contact Vader directly? Despite the asteroid field.
Answer: We don't know that the Emperor spoke to Piett directly. He might be relaying a message that the Emperor gave to another ship/location.
Question: On Cloud City, why did Vader surprise Han and the others in a dining room? Lando says that the Imperials arrived before Han's group. But they've had time for Leia to change clothes, change her hair style, and for her to ask people about C3PO when he is missing.
Answer: No answer is given. Maybe Vader needed more time to negotiate with Lando and wanted to ensure the group would feel "safe" and then be caught off guard. It's more about plotting, though. The scene is constructed to build suspense and doubt. Han thinks the friendly and charming Lando is trustworthy, but Leia is wary, especially after C3PO disappears. The group, and the audience, are then taken by surprise when Vader is revealed and Lando's true character and motive is exposed.
Question: Han wants to leave the Rebels because Jabba the Hutt still has a bounty on him. Why not stay and be protected by a large group of friends? Safety in numbers, basically.
Answer: There may be safety in numbers, but Han is not going to put his comrades' lives in danger to protect himself. He also doesn't want the bounty hanging over his head, or be constantly on guard for an ambush. The longer he waits to pay it off, the greater the consequences, which is what eventually happened. He wanted to pay it and be done. This also shows Han when he chooses to come back and help his friends win the battle.
Answer: In addition, Vader has a habit of showing more patience and tolerance for those under his command who came from similar poor backgrounds as him (in EU canon Piett was revealed to be from a common family that got displaced and then suffered under the Confederacy during the Clone Wars). Given Piett did exactly as he was told, and Vader likely considering him a second priority at that moment, it's not entirely out of character for him to give Piett a pass so he can go and sort through his conflicting feelings on what to do next.