Hi, Kenji
Good questions.
First, we need to differentiate between what DOT/IATA define as "hazardous" for shipping purposes and which chemicals actually present a real risk. We package several of the chemicals in a separate "regulated chemicals" bag, with the caps taped. That's to meet the requirements for shipping under the USPS 173.4 Small Quantity Exemption. Some of those chemicals don't really present serious risks. For example, the turmeric reagent is DOT/IATA "hazardous" because it contains isopropyl alcohol. In other words, there's 15 mL (one tablespoon) of rubbing alcohol in that bottle, but DOT/IATA defines it as hazardous because it's flammable. Other chemicals--notably the 6 M sodium hydroxide, 6 M hydrochloric acid, 6 M ammonia, 6 M acetic acid, and biuret reagent--actually are hazardous if you get them on your skin or in your eyes.
As far as storage, the usual method is just to keep them in a ziplock plastic bag. The only ones likely to emit noticeable fumes are the acetic acid, ammonia, and hydrochloric acid, which can be stored in one or more plastic bags, together or separately. The iodine solution is a special case. It does emit fumes (iodine vapor), but those are not particularly hazardous. They will stain anything they come into contact with. Once you've opened it, you might want to keep the iodine solution in a plastic bag on its own.