Fair chase
Challenge
Obession or passion
Respect (animals, landowners, etc)
Knowledge and Experience
Loves the outdoors/nature
Successful/Harvests (Joy, accomplishment, self satisfaction, Happiness)
Gives Back (Conservation)
Active (teacher, pass on the tradition, etc)
Companionship (deer camp, hunting buddies, etc)
Honest
Provider (food/Cloths, art)
Hardworking
Peace (woods, strees relief)
Evolving
Industry

I am sure many more or expansions could be added to these bullets, just some that came to mind.

To answer number two, there are many ways to do that now:
Camera
Game Camera
Video
Sheds
Passing (min. standards)
Hunting journals

I guess hunting is many things, more than a picture or mount or meat. It is a way of life for most of us. Good question, I am not sure how to accurately answer it, other that there are ways to take a piece of the animal without taking all of it and the one you take brings additional elements....that really sums up HUNTING!!!