If home-made bomb are illegal, then why is it suggested as a science project for my brother?

There are no universal laws on any subject. Criminal laws tend to come from the legislative branch of a government, such as parliament, or congress or a state legislature, or a dictator. No two criminal codes are the same. If you want to know if your nation, state, county or city legislature has enacted a law that prohibits all forms of experimental combinations of substances such that an "explosion" is possible, then start by mentioning what nation, state, county or city interests you.