Face puncher questions?

Borderlands 3 Amara the Siren
#1

Finally got the Face puncher and I have started one shotting in MM3 it’s an incredible buff that I only want to see increased.

How do I increase damage output. Obviously melee but with mod stats what classifies as damage output.

Gun damage?
Shotgun damage?
Melee damage? I know works

Can I build into all of these

I’ve noticed my legendary melee artifact fully procs also which is amazing. It’s a 80% radiation that applies a random element.

#2

Also Mayhem modifiers apply to what?

I don’t understand what is buffed…it seems my artifact makes it an elemental shotgun so would it be better with +elemental - normal bullets.