[eNotes editors are only permitted to answer one question per post. I suggest you post your other question regarding clauses and phrases in a new Q&A post.]
1) Grammar is the body of rules that guide the usage of language. This includes the way words work together, how they go together, how they build into sentences, and how words change based upon adding units of meaning (morphemes, affixes)
There are two approaches to grammar. Descriptive grammar looks at how people actually use language and its rules. Descriptive grammar does not result in rules being made as it only describes what is done, not what should be done. While prescriptive grammar is the rules developed over time about optimal grammar use. Prescriptive grammarians prefer these rules to be adhered to. There are positive and negative aspects to both approaches to grammar.
Syntax looks at words and the relationship of dependency between them that governs restrictions to their larger groupings.
linguistic syntax was the ways in which words and morphemes could be combined into larger units, particularly sentences. (University of Chicago)
2) So grammar looks at the rules that govern language use as a whole. Syntax focuses on the dependencies and restrictions in relationships between units of meaning as they combine to form larger units.