“After the suffering of his soul.” The phrase is idiomatic and means, “after he suffers” (cp. NIV2011, “after he has suffered”).
“he will see the light.” This translation follows the scroll of Isaiah found in the Dead Sea Scrolls and the Septuagint. There is good reason to believe the Masoretic text was miscopied at this point. The promise of Isaiah is that the Messiah will die, but will be raised from the dead, he will “see the light” (NIV: “see the light of life”). Jesus clearly rested on this promise when he gave up his life on the cross.