And this may not be entirely accurate or up to date information.
I have no idea what could get this solo, though I am guessing a lockpicking thief with gentlewalk or on a ghost timer could do it. You'll probably eat more than a few deaths though, figuring out how.

If you're talking a straight non-ghost/non-lock pick route, I'm not sure. Maybe a decked out invoker? Since I believe things crumble there, you have to be able to make the run with relative speed and kill enemies quickly. Most people I saw that got it did it with a group. Any area damager and a healer make it manageable enough. I think a bard + invoker could do it as a 2 man group. Bard goes in, tanks and heals, invoker follows and slaughters with pillar/nova. My bards made a few runs with other people, and it was usually a 3 man group.

Everything you would need to get the amulet can be obtained in the same area (I think)
Yes, there are numerous aggro NPCS in the area
I've made enough runs with people who knew how to get it, but if you explore the area, you'll get clues about how to get it. There is a reason certain things are in the area.

I'm pretty sure you can remove it without dying (otherwise stoneshatter would be an instakill on you), but it does damage and lags you on removal.

I imagine it's great on invokers, but most people that had it always avoided invokers because of stoneshatter (which would make it damaged now?). Most of the times it was a char that can see hidden. So as to avoid having it stolen if they removed it for an invoker fight.