Then you've been using one of the other definitions of faith. Faith also means trust or confidence (as Meow Mix has pointed out). But the definition we're interested in here is belief without evidence, as in the opposite of reason.
As in, superstition. I prefer to use that word for such a definition.
Compassion is acting on our caring for others. No compassion, no caring for others.I'm not sure where you get that idea. I don't have to have compassion to not hate or start conflicts and war.
Basically, a total lack of compassion is basically an indication of psychopathy.
Yeah, a world full of psychopaths. THAT'S a good world. :sarcasticReason can exist without compassion, and compassion is unnecessary for a world without conflict and hatred. I'm not sure where you get the idea that compassion is required for reason to exist. I'll agree that the best effect is for both to exist, but the world could be perfectly fine without compassion but with reason.
It's compassion that allows us to care that people are suffering in the world.