Kindle doesn't really play well with Calibre that much. You gotta jump through hoops just to get something done.
There should be a file in your Kindle with all your saved notes and highlights. It should be titled 'My Clippings', and under the 'documents' folder.
If you have whispersync enabled, you automatically back up all your notes/highlights for the books you have on cloud. You can try that out by installing the Kindle app on your phone. You should be able to see all your notes and highlights there too.
That should work for books that came directly from kindle and your 'send-to-kindle' documents. I'm not too sure about books you sideload tho.
There's also a plug-in in Calibre called 'Annotations'. I've only used it briefly, but it can import all the Annotations from your Kindle to Calibre. It's only 1 way tho. You can't send Annotations back to your Kindle.
As for the Kindle ecosystem. Everything works great if you mostly read ebooks bought directly from Amazon, or their 'send-to-kindle' feature. Everything will be saved on the cloud.
You can read about send to kindle here.
It's a really neat feature. I have books purchased from other digital stores and just send them to my Kindle. Only downside is you have limited font choices, and no xray (I don't really use that function anyways). You can also set up Calibre to send books to your Kindle this way. Just needs a few more steps, but really convenient.