According to the main characters, how should life be lived? What is going on in the late 19th and early 20th centuries to make people think this way?

This really depends on which character you are referring to. Humphrey van Weyden thought people's souls were eternal and that the life we lead, moral or immoral, in this mortal world echoes into the afterlife. In contrast, Wolf Larsen believes that life should be lived in the moment and for adventure: survival of the fittest. He felt it is acceptable for the strong to overcome the weak with brute force and cruelty.