You ask a lot of questions here, so I'll answer them all briefly, then explain, to help you understand in more detail. I feel sickened and defensive when I read Zinn's presentation of the United States, in this chapter and in others. Yes, the United States was an empire, and yes, it is still is in many ways.
Now, to explain those points in more detail, I'm going to start by going outside that chapter briefly. Thomas Jefferson referred to the United States as "an empire for liberty." He meant that as a positive thing, and used the phrase without irony. That was one of his goals for the U.S., and so it isn't wrong or damning for Zinn to say the country was or is an empire.
It is the nature of that empire that should give readers pause and make their stomachs upset. The United States was racist for a long time, consciously and intentionally racist. If you look at the country's internal laws governing race, you'll see that it was even legally racist. When Roosevelt mentioned that lynching Italian immigrants was a good thing, as Zinn notes in this chapter, that's at least partially racist. (There are other factors involved, like religion and theories of civilization.) Was the country a bully in addition to being racist? Again, yes. Look at the annexation of Hawaii, which Zinn mentions in this chapter. It was an imperial action, part of what made the United States an empire. It was motivated by trade interests and geopolitical maneuvering, and, in part, by race. Hawaii is far smaller than the United States. This is bullying in a very evident fashion. All of this also applies to American actions in Cuba that Zinn describes. What I find striking about the racism of this period is how it integrated with other factors. For example, take a look Zinn's brief mention of John Burgess in this chapter. He quotes a political scientist on the necessity for certain races and nations to civilize the world. (Burgess wasn't alone in this: Zinn uses him as an example.) In other words, some models of political science and history were telling the United States that acting in an imperial fashion, and basing imperial actions in part on race, was a good thing.
There's much more you could say on this topic, but that should get you started. Think about how you feel, and if Zinn is accurate.