Why not "den hele vej"?
Because "hele" is not a usual adjective like "hvid", for example. It is special, just like "alle".
In denmark is it only a few people who said "Præsterede" we will ask "kunne du løbe hele vejen"
Anything wrong with “klarede du at løbe hele vejen”?
“klarede du at løbe hele vejen” is absolutely correct!