I noticed that this is accusative. So it doesn't matter who is giving action to the object?
I'm assuming you've got the case name wrong :) I still have to look those up
Only thing that would change here is Дайте or Дай depending on formality level or number of addressees
Дайте is imperative. Also, 2nd person plural ("you guys"). Дай would be the singular form.
Чашку is Accusative. We are giving what? the cup (Accusative) to whom? to someone (Dative). Someone receives the result of the action (they would be in Dative, they are not in this sentence), and the action is done to the cup (it's the object of the action, it's Accusative).
Please note though that this word ordering is a bit obsolete and unnatural now, it's better to put "please" at the end or the beginning (as far as I understood, not a native speaker)