Is punctuation part of syntax?
Kind of, but not really.
Punctuation tells you how to read a sentence. (That period means to pause because a thought has ended, for example.) It helps clarify ideas and makes text easier to read. Punctuation is one of the major ways to identify the various clauses and other ins and outs that a sentence or selection may contain.
Syntax, on the other hand, is the arrangement of words in a sentence. For example, in English, the adjective goes before the noun. That's a rule of syntax.
So, syntax and punctuation serve similar functions, but they're not really the same thing, and neither one exactly fits into the other.