ADT bundle is very convenient for Android developers, as it comes with everything off the shelf to start developing an android app.
When you download the Android ADT bundle, it only comes (as of November 2013 )with Android 4.4 (API 19) and so you cannot develop for lower versions of Android.
Updating the package may be needed and so when you click on the Android SDK manager icon, you get the download icon.
When you check on the check boxes for the API(s), to download, and click install package, the needed packages should be downloaded and installed, but in some instances, it may not download and returns the message "Download interrupted: Connection to https://dl-ssl.google.com refused", "Done. Nothing was installed."
To solve this issue,
Click on tools --> options and a dialog for setting proxy appears. Set the proxy to the current network and click close.
That should solve your issues! If you have any questions, just comment below.