In order to get calibre metadata changes to register, you must delete the book from your Kindle and re-add it. It is a moot point if you have dual-MOBI ebooks, which cannot be reliably updated, but you really only see those when you make them yourself.
Covers in MOBI are an irritation. The MOBI format is old enough that it doesn't support the cover metadata, what instead happens is the image is added as the first page in the book. The Kindle will display the first image in a MOBI as the cover.
calibre will usually update all metadata including covers, but not for a format that does not support said metadata. To do so, you would need to do a MOBI-to-MOBI conversion.
In general, I would recommend converting to
AZW3, Amazon's next-generation Kindle format which support covers and CSS3, which can be edited directly by the calibre editor for book nerds
and in general acts just like EPUB but with a different format container.