I wouldn't worry about all that, I'd still leave the water out to let the chlorine to evaporate though. What's the EC of your tap water? You'll be running nutrients in your res to provide what's needed, hydro isn't like soil where your medium has nutrients to feed the plant and you can't just depend on the small amounts of nutes in your tap water.
Hydrogen peroxide is used to prevent root rot, root rot normally comes from high water temps in your res or crap bacteria in your res. If you have your water temp under control you'd prolly be fine without preventative measures but it doesn't hurt to prevent. There's two main choices when it comes to preventing root rot. Using Hydrogen peroxide or beneficial bacteria like Hydroguard, the expensive Great White or making what's called a "tea". Hydrogen Peroxide will kill all bacteria in your res, where beneficial bacteria will provide good bacteria to help keep bad bacteria away. You cannot use both at the same time or the Hydrogen Peroxide will just kill the beneficial bacteria.
I've used Hydroguard for over a year and am very happy with it.