Yes, but you make up for the efficiency by cooling a single person, rather than an entire room. At least, that is what it looks like.

Yes. It doesn't mention the size of the battery or how hot you get from lugging it around.

Having a very large distributed surface area could be key to drive the peltier cells at low current and get back some efficiency. The thermal contact with the body also helps by reducing the temperature gradient against the charges flow.

yes, i think what is novel is that they made it flexible and maybe that improves the efficiency