Napić się kieliszek koniaku

if in your book is napiję się kieliszek koniaku then there is a mistake your book.

"to co..napijemy się kieliszeczek naleweczki?"

napiję się kieliszka koniaku
napiję się filiżanki kawy

"Napiję się kieliszka" sounds as if kieliszek were the liquid you want to drink. Really terrible!

You will see many mistakes made by Poles which are a result of wide spread for years errors which found their place in colloquial language and are well rooted there.

"Napiję się kieliszka" sounds as if kieliszek were the liquid you want to drink. Really terrible!

Still I hear more times szklanki, kieliszka if used in such sentence than szklankę mleka:

Strzyga. However, you must know that it is very common to say "wypij sobie kielicha" or "napij się kielicha" or "chlapnij sobie kielicha". No one at their common senses, that is before any drinking, will ever say "wypij sobie kielich".

Could it be regional?

Unless you mean negative sentences, then it's ok - nie napijesz się szklanki mleka.

"Napiję się kieliszka" sounds as if kieliszek were the liquid you want to drink.

So in negative we drink the glass? ;)

In negatives we use dopełniacz :)

In negatives we use dopełniacz :)really? where's the logic and consistency?

It's not logic, it's basic gramar :)

Po upuszczeniu sauny, napij się szklanki wody

You're right, of course, but it's limited to kielich od wódka :) Would you say that "wypij sobie szklanki herbaty" sounds as good?

[For those who don't know: typically "napij się kielicha" is only an invitation to start drinking vodka in some bigger volumes.]

"Napiję się kieliszka" sounds as if kieliszek were the liquid you want to drink. Really terrible!

I feel imbecyle ;)

Po upuszczeniu sauny, napij się szklanki wody

Anyway, Google has seen weirdest forms and usages, which nevertheless doesn't make them all correct or even remotely acceptable.

When there was a tvp kultura short animated movies series about common Polish language mistakes there was an example with sweter that people allegedly say "swetr"... I never heard anyone to say "swetr". So maybe it works this way that in some regions somemistakes are more frequent than in other? How do you think?

Or wiater, like sweter :)

What about chłopaki and chłopacy? Is it true that both words are correct?

That should be applied then to "kieliszka case" because I've checked in google and many people write kieliszka as well as kieliszek

People often make inanimate things animate to express some kind of personal attitude to it or to behavoiur related to it or to make the sentence sound more friendly or funny

So in this case:
"Napijesz się kieliszek?" means "would you like to drink?"
while
"Napijesz sie kielicha?" means something like "do you want some of my good stuff? come on, let's have some good time"

Napijesz się kielich