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.
Then again, if I had the space, I would definitely dry them outside. Nothing beats the smell of clothes hung outside in the sun.