Disposal of the used acid/hydrogen peroxide etchant?
Disclaimer: This suggestion does not cover all aspects that may be required by your local regulations.

However, with any type of etchant, the most troublesome part is the one about the dissloved copper ions.

As long as you don't pour big amounts of strong basic or acidic solutions down the same drain, no heavy recation will start and cause dangers. Thinning any base or acid by adding large amounts of water will usually make them easy to handle. (Think concentrated acetic acid vs. salad sauce: Same chemistry, just a different concentration!) This applies to pure bases or acids. Your used etchant is more than just a hydrogen donor (acid), it contains copper salts!

Long story short: The pure etchant is usually not a very big deal, the copper ions are very toxic to anything in the nature (including yourself).

Related: Safety of making PCBs