Not "compulsory" but it is an essential modal particle that accurately turn your sentence into a suggestion. Without it your sentence may appear instructing or at least assertive.

No. But people use this word in real life.

Yes. That's what makes the sentence a gentle suggestion. It's the "let's." 我们去爬山吧 means "Let's go hiking." 我们去爬山 Means "We go hiking."

It said "let's" so I'd say yes

my two cents: 我們去爬山 is more imperative and would translate to something like "We are going hiking [whether you like it or not, it is happening]". Adding the 吧 makes it less imperative and more invitational, "Let's go hiking [if you want to]".

It's the particle of suggestion. This sentence is a suggestion.

In this sentence, it works.as a suggestion. Thus the english is "let's go...". Without the 吧, it sounds.more like a command or something that is definite

I think so. It changes the meaning from: "We are going hiking" into: "Let's go hiking!"

It still makes sense, although it may be more suitable when the action is starting soon and does not require more travelling (say, you come out of the base camp in the morning, and are about to climb a mountain.)