Sentence 1:

Ann says that she was going to Las Vegas with her boss, and the whole office was talking about it.

Ana said that: On one hand

she was going I see this more likely as a report or something like that. Imagine I am Ana. I am telling you that I am going to Vegas. I want to fly to Las Vegas. After that you tell a friend that I am going to Vegas in reported speech, so you must go one tense behind example:

Present simple = past simple

Present continuous = past continuous

will = would

past simple = present perfect

present perfect = past perfect