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.
I think this is either irrelevant, or inconsiderate if the point was to suggest "They should just be ok with this other thing I was ok with instead of what they want to do." without the excuse that what they want is somehow bad for everyone else. She's not raising chickens, and even the bit about the horrors of seeing "unmentionables" is ridiculous and deserves no consideration at all.