I’m afraid your initial line is entirely false. Abstract thought is completely possible without free will.
The second line is also false. We certainly could imagine things that didn’t exist. Just like mixing green paint and red paint can yield yellow — inputs can ‘create’ new things. Seemingly abstract things. Another thought: do you freely chose the dreams you create?
Jere’s reference to Wolfram’s cellular automata should also not be missed.
However, most of the rest is also false; but to skip to the end: I have absolutely no idea how you conclude (and therefore how to potentially refute or agree with), “Were we truly lacking free will, we’d all believe as you do without need to communicate it”.
I see no situation in which this would be true. I feel it would almost be the antitheses of that; the fact that there is no free will means there is a dire need to communicate and provide the right inputs, to move the overall system nearer to the truth.
People won’t just believe there is no free will, because there is no free will.