The leaves of the tree or the tree's leaves

Both are acceptable. A Google search for "the tree's leaves" using quotes (for an exact match) provides lots of examples.

Thank you! It seems like the general rules are far from waterproof

I am not sure what this means.

There aren't general rules, especially in English. That's just the way languages work. Any such "rules" are usually just customary usage. Customs change, and poets or bad writers come along and change everything.

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Perhaps you might be better to say the leaves on the trees:

The leaves on the trees would be softly sighing
If they heard from the breeze that you left me crying,
They'd be sad, don't be bad to me

"The leaves of the tree or the tree's leave "

"The leaves of the tree" is grammatically correct as in English we use 2nd case with human being.

I think you mean 'foolproof'.

First can work for a poetic/literature approach but I am under the impression the second version is the usual one. Since I am no native English speaker I am not sure if this is indeed the case. A2Ker's feel free to step in and correct me.

Forgive me but that is simply an absurd notion. The rules of English are described in many weighty tomes. If there were no rules you wouldn't be able to converse nor would you be able to write what you write.

Nor would you, and this is the salient point, be able to deploy nuances that we all deploy many times daily without the slightest conception of why we did so.

A writer, attempting to defend a cockamamie rule, said, "It’s always a dangerous thing when politicians get near the English language:".

Certainly not just politicians.

Both are fine. There are differences in register.

As per the grammar rules, with non-living things we use "of" and with living things we use " 's " for showing possession.

Not true. Bad advice. Read before posting.