Is semantics grammar
Semantics ... is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata.
I think your confusion comes from the last phrase, that is, does puncutation come under "signs and symbols"? The answer is no, because, semantics deals with the meaning, so punctuation would not come under this, as punctuation does not have a meaning, and does not denote something.
Punctuation comes under, syntax, which is:
syntax ... is the study of the principles and rules for constructing sentences in natural languages.
Thus, in order to construct a sentences, you will need to follow certain rules, including rules for using punctuation. Punctuation comes under syntax.
What doe spelling come under? I would say, "morphology":
morphology is the identification, analysis and description of the structure of morphemes and other units of meaning in a language like words, affixes, and parts of speech and intonation/stress...
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