2) Emmenez-moi y!
3) Emmenez-nous y!
4) Amuse-toi y!

Note, however, even though these commands are grammatically correct, they sound a bit strange to my ear. You'd much rather say Amuse-toi (without the y). Instead, là-bas is more common in this context than the pronomial y.

Agreed to your fact about the usage of là-bas instead. 

But there's a rule in this lesson - quoting it below - 

Adverbial pronouns en/y are placed after moi/toi/lui/nous/vous/leur and moi/toi become m' and t'

So, as per this rule, it is asking to contract moi/toi to m' and t' when placed before y or en.

Position of Double Pronouns in French - in affirmative commands in the imperative mood (L'Impératif)

Additionally, I found one example here -  Mets-t’y 

- https://www.lawlessfrench.com/grammar/imperative-mood/