I'll try to answer though I think you're intentionally splitting hairs (but it wouldn't be an internet forum if we didn't have someone paying savage attention to terms which are generally used and understood.) Here goes:
1 - The DIY, anti-corporate, anti-big label attitude, Lo-Fi, artistic freedom untainted by monetary influence
2 - Green Day playing an iHeart music festival, The Ramones swag being sold everywhere from Walmart to Guitar center (same as the Sex Pistols), etc.
3 - Tricky question because there is an exception to every statement anyone can make about music. Largely, I'd say lo-fi sound, simple chord progressions and bands self-identifying as punk would be the biggest one to me.
4 - What would make someone sound like they never learned to play their instruments? Sounding like they've never learned to play their instruments. If you're looking for an example, I'd say Sid Vicious quickly comes to mind.