What was the significance of the People vs. De Bour, Heller vs. DC, Thompson vs. Oklahoma, and Roper vs. Simmons cases?

In People vs. De Bour, the court held that there were four levels of street intrusion involving police and individuals. Level One is where the officer has credible reason to request information from the individual; Level Two, where the officer has a founded suspicion about criminal conduct; Level Three, where the officer has reasonable suspicion about criminal activity; and Level Four, where the officer has probable cause to detain and arrest the individual.
The next main topic involves Heller vs. DC, where a Washington, D.C. special police officer, Dick Heller, sued the District of Columbia for the right to keep a handgun at home. In its decision, the United States Supreme Court affirmed that the Second Amendment protected an individual's right to bear arms, even if that individual is unconnected to any state militia. Yet, the court also held that Second Amendment rights did not confer unlimited rights regarding firearm possession: it did not authorize anyone to carry any weapon, in any manner whatsoever, for whatever purpose.
In both the Heller and McDonald cases, the Supreme Court did not nullify all reasonable state laws regarding the use of firearms. It also did not establish any standard by which state gun laws can be evaluated. Read more about the Heller and McDonald cases at the Supreme Court blog.
As for the death penalty pertaining to juveniles, there are a few court cases you may be referring to. One is the 1988 Thompson vs. Oklahoma case, where the Supreme Court maintained that no juvenile under sixteen years old can be executed for a crime. In 1989, the cases of Stanford vs. Kentucky and Wilkins vs. Missouri led the Supreme Court to conclude that the Eighth Amendment does not prohibit the execution of juvenile defendants who are sixteen or seventeen years of age.
In the more recent 2005 Roper vs. Simmons case, the Supreme Court (in a 5-4 decision) held that it was unconstitutional to execute a minor (anyone under the age of eighteen) for crimes committed. The justices held that the execution of a minor violated the Eighth Amendment clause against cruel and unusual punishment.
https://deathpenaltyinfo.org/facts-and-research/history-of-the-death-penalty/limiting-the-death-penalty