You plumb a line for the wastewater back into the drain of your sink. So it goes down the drain. Most units create 3 to 5 gallons of wastewater for every gallon of RO/DI water produced, so that is something to consider. Even with that taken into account, it's still cheaper to make your own water than to buy it.
I think you should use RO/DI water even if you don't plan on having corals right away because using tap water often leads to algae problems, and you don't want to fight that battle unless you have to. And if you do keep corals and inverts down the road, it will be difficult to get your water in good shape if you have been using tap water all along.
You do not need to add anything to the RO/DI water before you use it. To top off for evaporated water, just add it straight to your tank. When you do a water change, the salt mix you use will adjust for pH.
