When Loveless Jr. demonstrates his atomic bomb, everyone (except for Loveless) looks at the blast, which should have permanently blinded everyone there. No one was even temporarily blinded.
Dr. Loveless Jr.'s base is in "Wagon Gap, Arizona." West and everyone else acts as if Arizona is part of the US, but Arizona would not be admitted until 1912. The movie is set in 1885.
Loveless has supposedly planted replicas of world leaders around the world. He doesn't need to further threaten governments with a letter of demands. He just has to issue the word, a la "Order 66." The hard part of replacing leaders with doubles was already done.