You will eventually want
Calibre, an ebook library management, converter and publishing tool (as well as web-scraper so you can grab sites for offline use.)
My suggestion: Download Calibre, let it manage your ebook library and fix up the .MOBI files (some are very likely not fully Kindle friendly), and use it to send them to the Fire via USB. That will make your whole Kindle life much easier.
And, as a special bonus, there is a very helpful Calibre forum here in MobileRead!