[ilovejedd]

• Do book formats matter (eg. mobi / azw3 / kfx) ?
  
  USB sideloading using Calibre send to device should upload the covers separately (to a hidden <drive>:\system\thumbnails folder) so format shouldn't have been an issue. It's only when using email to Kindle or copying via file manager/system when formats matter. Iirc, the Kindle will only read embedded covers from MOBI old [PDOC]. Caveat, you lose a lot of advanced features (e.g. boldness, custom fonts, etc). Might work for MOBI both, too, but it's been a while since I last tested that so I've forgotten what the results were.
  
  
• Do book ids matter (eg. must I set/unset isbn / mobi-asin) ?
  
  Same as above. Shouldn't matter when using Calibre send to device.
  
  
• Do book cover sizes matter (eg. Is there a maximum resolution) ?
  
  If there is, I haven't managed to hit it yet. I think all my book covers are at or below 1200*1600, though.
  
  
• Under what circumstances can/does the Kindle download it's own covers from Amazon ?
  
  Iirc, it worked for AZW3 with matching/correct Amazon ASIN. Never tried MOBI or KFX.
  
  
• Must I embed the cover image somehow (eg. I've read about epub to epub conversions) ?
  
  As mentioned, reading from embedded covers only works for MOBI old [PDOC] (maybe MOBI both, too).