I think "Laten we gaan zingen en dansen" would be better.
Sure that is fine as an alternative translation, but I don't thing it's better. Let's sing and dance! refers to now, not to the future.
I would use it in both situations but I did not think about that it can mean future too so I have to agree that "Laten we zingen en dansen!" is better.
Yup, that's the flexible Dutch tenses, now, future, who cares let's use it in both cases. :)
I think that would rather translate to: "Let us go sing and dance!"
Can this be said to either a group or an individual?
I think either would work, as long as the speaker is being included in the action/command.
Why "laten" and niet "laat"?
Because, in Dutch, the subject of the sentence is „we", which conjugates the verb to „laten"