Concerning the Hebrew idiom "writing 'Noah' with seven mistakes", how many letters does the word 'Noah' have in Hebrew and how does this sharpen the idiom's meaning?

First of all, the name "Noah" (the masculine, as in the one with the ark) is two letters long - Nun Het. Without any vowel markings, some might put in an extra Vav in there which would make it three letters. While both spellings are acceptable, the shortened spelling is understood by pretty much all Hebrew speakers to be the "correct" form. The phrase "seven mistakes" is sharpened further when one understands that in Hebrew literature the number 7 is often used to mean simply "many".

The expression hu kotev "noah" b'sheva she'giot, He writes the word "Noah" with seven errors, is a humorous description of a person whose writing is filled with the grossest of errors.
https://www.jhom.com/topics/seven/hebrew.html

In many Hebrew expressions, "seven" is used in exaggeration:
(al ta'amen bo, ki sheva to'eivot b'libo), "Do not trust [an enemy], for seven abominations are in his mind";
(Be'sheva aynayim tabit, v'titbonen el kol ha'nasah bah), "With seven eyes, look and observe all that is being done..."
https://www.jhom.com/hebrew/seven_h.htm