About The Drifter Response Battleship In C5s

I read about them:
Do they spawn only as capital escalations or do they spawn for completion of sites with subcap fleets?

Where do they go? Do they roam around the hole combat scanning for ships? Do they impact me when running other sites? Do they follow me around wormholes? Do they shoot my structures? Do they despawn or leave my hole after a few hours?

How can I fight them? What is their “doomsday”?