1) Kindle Collections plugin of course.
2) AZW3 is also known as "new mobi" because MOBI is mobipocket format 7 and AZW3 is mobipocket format 8. AZW3 is just a new and improved MOBI with proper support for CSS, cover images, embedded fonts... internally it is much closer to EPUB. (mobi7
predated EPUB.)
In other words the only reason to use MOBI is for ancient, legacy devices that never got updated to support AZW3. The K1/K2/DX(G) that is -- because even the K3 got support via a firmware update.