"Romans 9:15 means God is he who shows mercy to whomever he wills (God is judge). "
Romans 8:29,30 I think Romans 9:15 means it is God's choice to show mercy on the ones he foreknew, predestined, called, justified and will glorify.
And that his choice had nothing, at all, to do with mans will or works. Romans 9:10 "...and had done nothing either good or bad...."
Salvation is not, as you say, something man does or something man chooses.
Peace