How do you find the rare relics and do the relics DEACTIVATE when you move away from the target?

The rare golden relics are only found by luck - I think I collected three of them while I was completing my JA collections. She did have full archaeology skill and had completed both the JA aspirations, but I think that only gives a Sim a slightly better chance at finding rare things.

I'm fairly sure I found them in the temple treasure chests, but that's the only direction I can give. Once I'd found all the plates and assembled all the possible relics (which took a few Sim weeks), I was ready for my Sim to move on with her life, so I gave up on collecting the rest of the golden relics. Maybe one of her decendents will fill in the gaps.

The death relic can be activated multiple times. I can't remember if it has a cooling-off period, but it can definitely be used again. The danger with the wooden relics is that they can occasionally break while being used. The golden relics don't break.

Can they backfire and kill the sim activating it?

I was given golden relics from the tiger a few times.