1.) I think there's a bit of a chicken or egg problem - are the QBs above average or are the good teams making them look that way? Let's look at the QBs from the last 10 national champions:
Matt Flynn: I think you have to call him "above average" because he was drafted and stuck around in the NFL, but look at that team he was on. His 56% completion percentage is low by today's standards.
Tim Tebow: In my opinion, the best college QB ever
Greg McElroy: He looked pretty good, but who wouldn't look good throwing to Julio Jones?
Cam Newton: Single handedly brought his team to a national championship.
Aj McCarron: Like McElroy, seems pretty good, but how do you not look good on that team.
Jameis Winston: Very good
Cardale Jones: I consider him about average. And this is what I mean about how being average can work. He wasn't an above average runner or passer, but won a national championship and looked pretty good doing it.
Jake Coker: Again, looked decent, but was he anything special?
Deshaun Watson: Outstanding
So Tebow, Newton, Winston, and Watson are all clearly above average. The Alabama QBs are tough to tell, but let's call them at least above average and include Flynn with them. That leaves Jones and Coker as players I would consider "about average." So about 20% of national championships are won by "average" QBs.
How many of those national champions had average offensive or defensive lines? The only team without a bunch of draft picks along both lines was Auburn
2.) LSU's QBs have been well below average. Of course a terrible QB (and a head coach who doesn't understand basic clock rules) can lose you games.