Does "neath" have any standalone meaning?

Neath or 'neath does have a standalone meaning, but as you will see here, it simply means beneath. It appears in poetry usually, I suspect, when beneath or underneath would add too many syllables to the line.

You can see its use in Google Ngrams here compared to beneath (most common) and underneath. It is quite rare, and declining:

Neath comes beneath underneath, which come underneath beneath!

In Old English, you could create a verb from another word by prefixing it with be-, as in become, besiege, bedaub, befriend.

beneothan meant "make far-down", while the related neothera meant "more far down".

Their shared root, neothan, that had it survived we could expect to have become neath and to mean "far-down", dropped out of the language, and meanwhile beneath became the preposition it now is, while nether became close to what that shared root once meant.

Meanwhile underneothan (under the low-down thing) became underneath.

'neath as a contraction comes from beneath, rather than beneath coming from neath as you may expect, though they all share a common Old English root.

Yes. It is an aphetic variant of the preposition beneath It was first used in 1787. As in:

• He then placed jack stands under neath the rear suspension.

• Neath his calm surface, there was seething anger

It is now considered archaic and/or poetic. It is often spelled 'neath. It is frequently preceded by the word under.

It seems that 'neath' is a development of 'nether', and has similar (though archaic) meaning.