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.
Do you not have space for a washing machine either? In many apartments in the US the dryer is stacked on top of the washing machine. It doesn't consume any additional space.
It would not have fit in my first Parisian flat. ( to be fair… nothing was really fitting there )
Also when you rent a unfurnished place in France it’s empty-empty.
There is no frige/oven/washer/drier combo like in a US non-furnish rental.
In my personal case I saw a drier as yet another anoying piece of furniture I would have to deal with when moving