Short answers, pulled from the story.
Peter Debye won the Nobel Prize in Chemistry in 1936 for his contributions to the study of molecular structure, primarily his work on dipole moments and X-ray diffraction. The prize recognized research that began with his 1912 application of dipole moment theory to asymmetric molecules.
The Debye-Huckel equation is a method for calculating activity coefficients in electrolyte solutions. Debye developed it in 1923 together with his assistant Erich Huckel as an improvement on Svante Arrhenius' theory of electrical conductivity. Lars Onsager refined it further in 1926.
Debye signed a December 1938 letter as chairman of the Deutsche Physikalische Gesellschaft requiring Jewish members to resign their membership, closing with the words Heil Hitler. A 2006 Dutch book by Sybe Rispens brought this letter to wide attention and prompted Dutch universities to consider removing his name from institutes and prizes. Multiple historical investigations, including a 2007 NIOD report and a 2008 Terlouw Commission report, concluded he was not a Nazi sympathizer or collaborator, though the NIOD described him as an opportunist who adapted to the political systems around him.
Yes. Debye and Dutch colleagues helped the physicist Lise Meitner cross the Dutch-German border in 1938-1939 to escape Nazi persecution, at considerable personal risk. Meitner eventually obtained a position in Sweden. None of the Jewish scientists who knew Debye personally, including Meitner and James Franck, objected when he received the Max Planck Medal in 1950.
Debye became a professor at Cornell University in Ithaca, New York after leaving Germany in early 1940. He chaired Cornell's chemistry department for ten years and became an American citizen in 1946. He retired in 1952 but continued research until his death and is buried in the Pleasant Grove Cemetery in Ithaca.
Numerous concepts bear Debye's name, including the debye unit of electric dipole moment, the Debye model of heat capacity in solids, the Debye length and Debye shielding in plasmas, the Debye-Huckel equation for electrolyte solutions, the Debye-Waller factor in X-ray diffraction, and the Debye-Scherrer method for X-ray powder diffraction. A lunar crater, a minor planet (30852 Debye), and several other physical quantities also carry his name.