Please tell me something about the general practice of thirds, both diatonic and chromatic; also, about those in the first movement of the Grieg Concerto.

As the playing of passages in single notes requires a close single legato, to do double thirds requires an equally close double legato. As to the exact details of legato playing I may refer you to my book, "Piano Playing," where you will find the matter discussed at length in the chapter on "Touch and Technic."