It's always required that you select the app, at least for me. I suspect that you have a mix of formats. I don't have any mobi/azw books downloaded to CC on my iPad, so I don't get Kindle as a selection. I do get Marvin, iBook and Goodreader since I have a mixture of epub and PDF.
As far as the covers go, try using the wireless connect rather than the content server. It's a bit more inconvenient since selecting and download is done from the mac rather than on the iPad, but it seems to have more capabilities to sync up information such as book covers, meta data and the like.
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