"Space" isn't a place, it's a velocity. Even if you throw something really fast in space, it will eventually come back to you unless it hits something else.
This is not correct. Space is a place. And when people say send it into space they typically mean the sun. Although any uninhabitable body would do fine as well. There are plenty of those.
The amount of energy required to send something into the sun is quite high. It's not like driving 93 million miles, you have to change the orbit of the waste away from Earth's orbit.
I didn't say it was a good idea, but that's what people mean. Although it isn't unreasonable to imagine space elevators and slingshots a few thousand years from now.
