1. Why were nuclear weapons made?
The first nuclear weapons were made through "The Manhattan Project" in the United States. Nuclear bombs were invented by the US through the Manhattan Project to beat Nazi Germany to the weapon. If they didn't do so, it was understood that Germany would win WWII.
"The Manhattan Project was an unprecedented, top-secret World War II government program in which the United States rushed to develop and deploy the world’s first atomic weapons before Nazi Germany."
Manhattan Project - Manhattan Project National Historical Park (U.S. National Park Service). (n.d.).
The making of the weapons, of course, wasn't a single event but a series of events spanning years and years, starting in 1895 with the discovery of Uranium, and continuing to 1945 with the detonation of the test bomb "Trinity" and the bombing of Hiroshima and Nagasaki.
2. Are nuclear weapons still being made?
Yes, actively.
While total global stockpiles are far below the Cold War peaks, active military arsenals are growing again. Major powers like the US, Russia, and France are actively remanufacturing aging warhead components, upgrading electronics, and building updated weapons. China is also undergoing a rapid, large-scale build-out of its nuclear force, while North Korea, India, Pakistan, and Russia are actively increasing their stockpiles.
However, major powers have agreed to stop testing nuclear bombs in the 1990s. (North Korea is the only country to detonate a live nuclear bomb underground this century, its last being in 2017.)
Today, countries like the US, Russia, and China use supercomputers to model nuclear reactions and run "subcritical" tests. (Small experiments using real nuclear materials that are kept just below the limit needed to trigger an actual explosion.) While they don't actually blow up warheads, nations regularly test-fire unarmed missiles designed to carry them into the ocean to make sure they fly accurately.
Sakura