"Drink your milk, my son."
Translation:Trink deine Milch, mein Sohn.
No. This is because the person who, we can reasonably assume, is being spoken to is mein Sohn. The command is being directed at him, meaning he is what will drink the milk. Deine Milch is the accusative because it is what is being drunk.
If you put mein Sohn in the accusative, you are saying that the son is receiving the action of the verb, not performing it, therefore he would be what is being drunk rather than what is doing the drinking.
It makes more sense if you remove deine Milch.
Trink meinen Sohn -> Drink my son.
Yes. This is the imperative, which, as in English, requires a special verb form.
Trink(e) -> du
Trinkt -> ihr
Trinken Sie -> Sie
This pattern generally follows, although some verbs may not be the same.
In English, for example, we say Don't be sad not Don't are sad or Don't am sad or Don't is sad.
In other words, we are talking directly to someone and giving them a command. 'You drink water' would be in the way you have been learning so far. 'Du trinkst Wasser'.
What is in this skill is ordering someone to do something, like 'drink water', which would be 'trink(e) Wasser' (the -e on the end of 'trink' can be included or excluded).
In English, the second person and the imperative form are the same, but in German, they are different. Once you learn these new endings, it will be easy.