We already radiate heat away just fine in space, it's just a matter of how much space do you need to use to do it and all the implications of what that would mean for any given satellite. I wouldn't call it free, because you need the hardware to do it and the extra weight reduces the payload capacity of whatever you're sending up, but we can do it.

Starlink also uses laser links to talk to each other which these satellites would also use. How they work can depend, but generally they bounce around in space until they can't, and they might come back down to land, to move somewhere else over fiber to another ground station until they can go back up to reach you. But the more laser links the less they have to come down for technical reason, but they might still come down for bandwidth reason. I don't really know how likely it is that any given connection is point to point.

Example of what could happen.

Your dish -> starlink -> starlink -> ground station -> Google -> ground station -> starlink -> ground station -> starlink -> groundstation -> starlink -> starlink -> your dish.

Fiber is still the better option on land if you can get it there, but there are a lot of places it's never going to get laid, and will never be in the air, or on bodies of water.

Edit: Corrections on the laser links with an example.