"Let's go further."
Does this not mean "We go further"? I can not see where the "Let us" or "Let's" bit comes in?
I can't say, "Idziemy dalej"? When we used to walk the dog together, my wife would often tell the dog, "Idziemy!" to make it move. I figured that it would work like that here. Maybe this is because people often talk to pets and babies differently than to adult humans.
"chodźcie" -> 2nd person plural imperative. 2nd person singular imperative is accepted as well. I know that from the point of grammar they are different, but frankly, they would rather be translated the same way.
In such a sentence, if you say "chodź(cie)", it really does mean that you are going as well. "Idź(cie)" would just be "(you) go".