Yes, God gave us all brains... :)
No, but rather, as Paul says, "it (God's election of certain individuals to salvation) depends not on human will or exertion, but on God, who has mercy" (Romans 9:16). Otherwise, grace ~ which is unmerited favor ~ is not really grace. And this is precisely what Paul says shortly thereafter, saying, "...if it is by grace, it is no longer on the basis of works; otherwise grace would no longer be grace" (Romans 11:6). We should note here that Paul in no way refutes free will; he does absolutely nothing of the sort. But he does say that our salvation doesn't depend on it ~ doesn't depend on our will or working ~ but on God's election.