You are right there, about Grace, always capitalize "Grace' It is surely God and therefore from God, as Holy Spirit. It does make one regenerated, yes! Yet there has to be a reason one receives Grace while another does not, and it would be so with Adam, who lost his faith, so shall we find faith without seeing. Jesus had told Thomas. "believe without seeing".
'surely', that does look right?
Election provides the saints with Grace, but Grace does not inform us of the whys of Divine Election.
Such is known only to God.