Yes, the evaporating cools down the room, though I can't say I ever noticed it. In terms of energy efficiency compared to a dryer, it's much better in summer, and not much better in winter, though you get a humidifier as a freeby.
Yes, it's a chore, a full load takes about ten minutes to hang, and it's real boring work.
Definitely not possible in the flat we live in during the winter unless we run a dehumidifier.
For this discussion is means that in London the indoor climate is livable, but terrible for trying clothes, while in Norway the indoor climate is nice and drying clothes indoors is helpful for adding humidity.