That definition could apply to a whole sentence (or novel), or a sound like "pfft." Or it could be an initialism, a movie rating, or an analyzed string of DNA. All these and more are letters arranged in a way as to convey thought.
Ah, well that explains away one of the examples... You must be right! (I'd argue that the analysis of DNA is a thought/type of understanding, rather than the essence of a living thing, but that quickly gets towards another linguistic argument of Sausserian structuralism vs post structuralism.)
The first two do not fit the description, as neither is conveying a thought. Those aren't words. They're onomatopoeias.
They do convey thoughts, which is why you know what they mean.
They're not onomatopoeia, because they aren't made to reflect sounds (though the first one reflects a sound a person would produce with their vocal tract, those aren't usually called onomatopoeia).
Spoken words are still made up of letters, even if they're not written down.
Spoken language came before written language. Words existed long before letters were invented. So then letters making up words can't be the definition of words because words existed before letters existed to "form" them.
Just because they aren't roman letters, does not mean they aren't letters. Cuniform and hieroglyphs are just a different kind of letter.
They don't need to be Roman letters, but many written languages don't use letters. I'm not sure about cuneiform, but I know that not all hieroglyphs are letters. Chinese is another written language that doesn't use letters, for example.
They do convey thoughts, which is why you know what they mean.
I'm sorry but even as a joke, this is just way too wrong. The examples given of "Mmmmmmmmmmmmmmmmm" and "Aaaarfgfhfhrhhhh" have no meaning. They are, at best, sounds. Making them onomatopoeias.