Dyson spheres could exist – but there's a catch

I have another simple catch, how the energy harvested by a Dyson Sphère is supposed to be transported to the planet where people live ? I suppose a direct cable is out of question, and I don't think wireless eletricity is possible, so what does remain ? Batteries charged and after transported from the Dyson Sphere to the planet, and when empty, returned to the Dyson Sphere ?

Or maybe I'm missing something.

Even assuming you could build one, the artificial gravity created by the rotation would only exist around the equator, diminishing to nothing at the poles. So only a natrow band would keep people and their stuff from floatin ofr into the bubble eventually falling into the sun.

How do Dyson sphere proponents solve this?