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.