Short answers, pulled from the story.
The first recognized Neanderthal fossil, known as Neanderthal 1, was discovered in 1856 in the Neander Valley of Germany. Local schoolteacher Johann Carl Fuhlrott identified the bones in the Kleine Feldhofer Grotte and passed them to German anthropologist Hermann Schaaffhausen.
Neanderthal brain volume averaged 1,520 cubic centimeters for males and 1,300 cubic centimeters for females. These measurements are significantly larger than the averages for all living human populations.
The average height of Neanderthals was 164 centimeters for males and 157 centimeters for females. Their body mass index ranged from 26.9 to 28.3, making them stockier and more robust than modern humans.
The first Neanderthal genome sequence was published in 2010 and strongly indicated interbreeding between Neanderthals and early modern humans. Neanderthal-derived genes descend from at least two interbreeding episodes outside of Africa, one about 250,000 years ago and another 40,000 to 54,000 years ago.
The extinction of Neanderthals occurred roughly 40,000 years ago with the immigration of modern humans. This extinction is ascribed predominantly to competition with modern humans, their low population, and resulting mutational meltdown.