With nits, fleas and other parasites I find prevention is better than cure.
With bugs and spiders in the house I'll rescue them. Even go and rescue spiders from my stepmothers house before she finds them and goes on a blitz. My manager at work thinks I'm crazy when I go around rescuing all the worms that wriggle their way in to the stable block when in rains. And moths I also rescue a lot of moths haha.
I try to avoid killing anything where possible but there is a line you have to draw.
With nits, fleas and other parasites I find prevention is better than cure.
Ditto.
As for bugs, I'm another who will take them outside, not kill intentionally etc. It is impossible to be completely cruelty-free - living a violence-free life is about being cruelty-free as far as is possible and practicable.
I kill insects - flies, mosquitoes, ants (if they're in my kitchen, i don't go out of my way to kill them outside), I don't kill pests in the garden, i try to use natural methods to discourage them. I take spiders outside, I rescue worms and snails on the footpath.... something that amuses my friends greatly.
they are just so cool. Good for my vegie patch too. 
