Better would be "Do you already have a beard?"

I think this depends on how well it matches the other translations.

Have you had a beard before?
Have you a beard already?
and
Do you already have a beard?

are all valid English sentences, but they all mean something different.

What's the difference between "Have you a beard already?" and "Do you already have a beard?" ?

I can't imagine a native English speaker saying the former, and though it may be grammatically correct, it doesn't sound natural.

I should really emphasise that the original
"Have you had a beard before?"
is the most likely sounding sentence of all of them. Does it really not match any of the translations?

I think the original did match the french well (if I'm not mistaken)...that leaves 3 other languages to check against

Well I would say that the German and Spanish _don't_ match the original, but match the latest: they're both in the present tense whereas the original is in the perfect tense.

The Spanish version matches the latest version, "have you a beard already?", and I think the French and German translations too; but the Portuguese one matches "Have you had a beard before?".

"Have you a beard already?" is fine, IMO. It's terse, and maybe a bit poetic, but it sounds nice.

It didn't sound natural to me, so I adopted it and took a third route.