Is it all right to say "all men have one head"?

Why shouldn't it be "Everything has two handles"?

"All" seems to sound better. A lot of the terms and expressions coined last time, had the word "all" instead of "every". E.g."All things must pass." "All creatures great and small." "All roads lead to Rome." "All's fair in love and war." etc.

"All" is used just because it seems to give a better sound.

2.Is it grammatically correct to say "all men have one head"?

Yes, it's grammatically correct. It doesn't mean that everyone has one head in total. It means that everyone has one head for each person. If this still sounds wrong, try:

All men have only one life.

The meaning should be pretty clear.

Yes, it's quite grammatically correct.

You want to say:

Every man has one head.

If you say

All men have one head.

it sounds like they are all sharing one head.

You can get away with "all things have two handles" or "all men have two faces" because here, "handles" and "faces" are metaphorical. But even so, there are more Google hits for "everything has two handles" than for "all things have two handles".

First, "Everything has two handles" says that all-that-is, or the universe, has two handles. The sentence is grammatically correct but not highly meaningful. The variant "Every thing has two handles" also is grammatically correct and more or less equivalent in meaning to "All things have two handles" except that using Every avoids the ambiguity (noted below) when All is used.

Second, while "All men have one head" is grammatically correct, it is semantically ambiguous because of ellipsis. Most people will take it to mean "All men have one head each", but as noted in the question, it could be taken to mean "All men have one (shared) head". Mostly-unambiguous rephrasings with various meaning and nuance include

Every man has one head.
Every man has his head.
Each man has one head.
All men have one head each.
All men share one head.

The phrasings "All men have a head" and "Every man has a head" are grammatical but like "All men have one head" ambiguous, as head could mean either one head each or one shared head. "All men have heads" would usually be taken to mean "Each man has his head" but does not preclude people having multiple heads.

It is grammatically correct. The meaning is ambiguous. The writer could be saying that all men have one head each, or that all men share a single head. I think we would pretty quickly guess that in this case that means one head each unless this sentence is in a science fiction novel. But it's easy enough to imagine a sentence that is truly ambiguous. Like, "Union rules say that all members of the union must work for only one company." Does that mean that no one is allowed to have two jobs, or that they all must work for the same company?

"Grammatically correct" and "clear and unambiguous" are not the same thing. In this case, I'd avoid a construction like that and say something more like "All men in the world share a single head" if that is what you mean, or "All men have only one head each" if that's the intent.