"He likes beer too much and drinks as often as possible."
Translation:Li tro ŝatas bieron kaj drinkas kiel eble plej ofte.
It's perfectly fine to 'trinki' alcohol, it just depends on the circumstance.
For the most part 'drinki' indicates intention not necessarily excessiveness, ie drinking alcohol with the intention to get drunk.
Meanwhile, you would not use 'drinki' for someone simply having a sip of an alcoholic beverage to taste it, ie a wine taster, or a curious teenager at a family function and also drinking the wine during communion at church. Here 'trinki' would be better.
"kiel eble plej..." is sort of a fixed expression thing (sorry, don't know the technical term). So you say things like "kiel eble plej rapide", "kiel eble plej multe", "kiel eble plej longe" and "kiel eble plej ofte". If the 'eble' follows the 'plej' I don't think it makes sense.