Thanks for writing!
Though I love a lot of what I've heard from this person, I don't agree with some of his views on "everyone in the world being redeemed". He has made some assumptions from Romans 5 and 2 Corinthians 5 to suggest that the "all in Adam" become the "all in Christ", and yet the fact is that nothing from Adam passes into Christ, but instead was all killed through the death of Christ. The fact is that since all were put to death through Christ then anyone who is in Christ is a new creation. Paul's point was never intended to convince us that Christ is in every man, but that we would know that all is dead outside Him ... and that, therefore, we no longer have any basis upon which to view people after the flesh, because God doesn't count men's sins against them. Dead is dead, alive is alive.
Yes, as you say, there are many references made by Paul that contradict that viewpoint.