I remove my hop bag a minute before I turn off the burner and squeeze the wort out of the bag by pushing the bag against the side of the kettle with my brewing spoon. Doing it a little before you cool it off will disinfect any nasties that I may have introduced with my spoon.
I pull mine, but due to my setup, it would be a pain to chill with the bag in. Still trying to find a good way to get my IC into the boil for 10 with a strainer bag stretched around the rim of the pot. :/
Really depends on what I'm brewing. If its a hop forward type of IPA or pale, i will leave it in while cooling. It it's not a hop forward type of brew, I take it out at flame out. I use a hop spider for the pellet/leaf hops, fwiw.
I leave the hop bag in during the duration of my slow chill, let it hang drip, maybe squeeze it a tiny bit, and then remove/discard it prior to aerating and pitching the yeast.
I have thrown them in loose. While they have eventually settled out, I feel like I get more wasted wort trying not to get the hop debris in my fermenter than if I use bags. I know it's better for utilization to forgo the bag. Maybe I should just plan for the extra loss. Also I worry about extra bittering/harshness/astringency from the beer sitting on hop debris for a long time.