Answer:
No. You do not need to provide proof of hunter education when you apply for or buy a license, but you do need to show your card if checked in the field when hunting with a firearm.

Yes. States recognize other states' hunter education certificates.

Question:
I'm trying to find some buddies to apply for big game with me, because you have a better chance of drawing on a "party application" — right?

Answer:
Sorry. Wrong.

A party application is assigned only one number in the drawing, just like an individual application. If that number gets drawn, all members of the party draw. You hear it said that each member of the party is in the drawing individually, and if one member gets drawn then all in the party get licenses, but that's not the case. A party application has no more chance of getting drawn than an individual application.