Christians must be able to drink alcohol, isn't that what they do when taking communion?
Nope - at Communion Christians - and particularly Catholics - genuinely believe that they are drinking the blood of Christ. At Communion, the bread and wine are transformed by The Miracle of Transubstantiation into the "actual body and blood of Christ".
Jesus turned water into wine, and he served it at the last supper.
Nope - he did this at a wedding and only when pushed. The guests were surprised that the host saved the best wine (Jesus' stuff) for the end. This was not at the Last Supper.
At the Last Supper Jesus instructed the disciples to drink the wine and break bread together in remembrance of him. that might be where your confusion comes from.
I'm not a Christian by the way. I'm a Humanist - it's just that I listened in skool!