Is syntax how well you manipulate words when saying something?
Diction is the choice of words to express a thought. Syntax is how those words are put together.
The question is : Is syntax how well you manipulate words when saying something?
I don't know that I'd use the word "manipulate"! I'd have chosen something different, more like "use" or "choose". The choice of words to express an idea or question is called diction.
The order we put those words in is called syntax.
The more complicated the thought or diction choices, the more complicated the syntax needs to be to accommodate them. For instance, I can express the thought:
He sees him - basic syntax of Subject + Verb + Object
But if I want to wax poetic and choose far more complicated words and place them in an order to create atmosphere, I could write:
P.I. Matt Shafely, on assignment to locate the rare and quite valuable Tibetan Tree Cat, peered through the hedge and spotted it asleep at the foot of a redwood.