You're using some terms that don't make any sense.
Calibre != Kindlegen
If you're using Kindlegen then you're not using Calibre - just use your ePub output from Sigil and convert using Kindlegen.
If you want to use Calibre then use Calibre to convert from ePub to mobi.
Calibre had some issues in the past creating mobi files that allowed Amazon to add DRM, but that's been fixed for many months. Depending on the specific formatting of your ePub either Calibre or Kindlegen might do a better job. In general I've heard more positive feedback for Calibre.
Regarding previewing the book, traditionally Kindle Previewer was the best way to get an accurate preview of how the book would look on a Kindle. This is probably no longer the case with the Kindle Fire, and you'll probably need to ask around on the Kindle forums or other places to find out what the best way to view these are - my guess is it would render identically as the Kindle App on Android.
Lastly, Amazon has a history of trashing images in ebooks to save their whispernet costs - I'm not sure where in the distribution process this happens, but every mobi I've ever gotten from Amazon has always had massively/horribly compressed images compared to the original ePub sources - not sure if they're going to relax on this stance with the Kindle Fire.
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