In English it would be polite to ask:
"Can I have some juice please?"
"May I have juice please?"
But "give me juice please" would sound a bit rude in English. Well, unless perhaps you say it with an open smile in response to "what will you have?"
So this is demonstrating both the accusative and dative cases: сок doesn't change because it's inanimate masculine, and мне is the dative form of я? The same as saying "Give juice to me, please". Luckily I encountered the dative case in German already, so this makes perfect sense :-)
Certainly it would be correct to use these sentences like that. But if you just were asking someone to take the juice that is on the table and pour some into your glass I think it's still appropriate to say сока. If you wanted the whole container of juice though you wouldn't use сока.
I guess I'm missing something. The infinite form is Давать, right? And many websites list 2nd person plural as даете. For instance, http://learningrussian.net/conjugation_give.php http://www.russianlessons.net/verbs/26 http://learningrussian.net/conjugation_give.php
So what's the deal, why does it appear to be using the wrong conjugation form?