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"du trinkst" is the familiar "you"-singular. "Sie trinken" when translated as "You are drinking" would be the formal "you" or used when speaking to a stranger- but still singular. "Ihr trinken", I think is the plural formal for "You, meaning many you's, are drinking". I'm not sure if what I have inserted here is completely correct or not.
Du is singular informal you. Du trinkst = you drink, where "you" is one person.
Ihr is plural informal you. Ihr trinkt = you (all) drink.
In addition to that, there is also the formal you, which is the same for singular and plural and follows the conjugation of third person plural with capitalised pronoun: Sie trinken = you (ladies and gentlemen) drink.
Ich trinke Wasser. I drink water.
Du trinkst Bier. You drink beer. (you = one person, we are familiar)
Er trinkt Wein. He drinks wine.
Wir trinken Milch. We drink milk.
Ihr trinkt Apfelsaft. You all drink apple juice. (you all = several people, we are familiar or they are children)
Sie trinken zu viel. They drink too much. OR You drink too much (you = one person but being addressed formally)
I hope this helps.
"I'm drink" is bad English. It's either "I drink" (as in I drink beer on Friday nights - repeated action) or "I'm drinking" (I'm holding a glass of a beverage and drinking from it as we speak).
"Your drinking" also doesn't mean "you are drinking". That would be "you're drinking".
In theory, it should be correct to say "I drink, you are drinking", but there would be a meaning of "I have a beer occassionaly, you are an alcoholic" and the German sentence doesn't have this distinction.