Doing what you believe to be right despite severe personal consequences.

The subjective part is that what you think is right and what others think is right differs. You're only a hero if most people agree that you did the right thing I guess.

You probably need to be decently upstanding, too. Some might say the child rapist in your example committed a heroic deed by dying fighting a wildfire but people would not call them a hero.

I think sometimes people can be heroes without extreme sacrifice, too. For instance, I would call Fred Rogers a hero solely because of his positive impact on others.

Generally going out of their way to help others despite the risk of personal harm or because the amount of work involved was significant.

Someone who spends their lives making other people's lives better for no personal benefit is a hero.

Someone who rescues someone despite the possibility of danger to themselves. Not those that do it in a stupid way that makes it more dangerous for everyone, but those who do it when the safest way is still pretty dangerous.

I need a hero
I'm holding out for a hero till the end of the night

There's a whole book about this. Well, partly about this. Hpmor.com. Have fun. I think that part might start at chapter 66.

This is entirely subjective. IMO it's self sacrifice for the good of all. Saint Rossman and Saint Luigi are good examples. Rossman is incorruptible and dedicates his life to fighting for us, and makes a point of publicly mocking companies when they try to bribe him.

The why is important. The weapons manufacturer who revolutionised farming with nitrogen fertilizer is not a hero, even though he saved millions.

The general character isn't. Linus is an asshole, but he gave us freedom.

Its subjective. Theres people that think trump is a hero