In many installations they can. Please view the installation guide found under the header "Info and guides" on the Home Depot product listing page.
As this is a toilet with a macerating pump, the answer would be where ever the end of the pumps discharge pipe is piped to. Typically that is into the plumbing stack of the home. And typically that is piped to either city sewage or a septic tank.
No the manufacturer recommends that the pump is installed directly behind the toilet.
No, the pump is not automatically activated when water from a shower or sink enters the pump chamber.
What is the distance from the wall to the front edge of the round boll?
To put in a toilet, shower and sink where one is not currently or where you can't or don't want to bust up a floor. For example, If you have a basement that doesn't currently plumbing/drain system installed in the concrete for a bathroom, you don't have to break up the floor to install a drain system. This will allow you to pump the waste up to a location that has access to the drain/waste/vent (DWV) system.
Yes, this system does require an electrical connection to power the pump.
Alex: Thank you for your inquiry with HomeDepot.com.. The Macerating Pump does require an electrical connection. We hope this information is helpful, we appreciate your business.
You can but you would need to do that through a store as a special order.
I am not exactly sure what you mean by water hook up. The toilet will need a water supply just as a conventional toilet will and the pump will need a conventional sewage system to pump into. This is not a composting or water less toilet