The only thing I see is that "not ever" is the exact meaning of "never" and "never drinks" sounds more natural.
Also, I could be wrong on this, but it seems your translation is creating two individual verbs: "he does" and "to drink" rather than the single verb of "he drinks".
Double negatives don't mean the same thing in English that they do in Italian. In English, "my brother does not drink nothing" means "my brother drinks something". The the two negations cancel each other. In Italian, one, two, or even three negations don't cancel one another. They reinforce the negative. So, ""mio fratello non beve mai" just means "my brother never drinks".
n.b. The above applies to negations of a single verb. If each negation is attached to a separate verb, then we get a canceling situation like in English.
"Non credo di non essere capace" has roughly the same meaning as "credo di essere capace".