Ok, but Chewie growls at a lot of people. Does Han shoot all of them without hesitation?

Yeah but the Stormtroopers showed up after the fact, behind Han and company. The door opened, Vader stood up, Han immediately shot at him. Then Boba Fett walks up behind Vader and the Stormtroopers show up behind Han.

This reminds me:

1) Why did Han shoot at Vader in the Cloud City dining room? That’s the first time they had met. Why would Han even know who he is on sight? I never got the impression that Vader was a galactic celebrity.