Happy to help, will start from your last question first.
What is the Joomla Framework
Most of the information about the Joomla Framework is not valid anymore, and the information on
http://framework.joomla.org would better be removed to avoid further confusion among developers.
At present the code found at
https://github.com/joomla-framework provides a set of PHP libraries that are slowly being adapted by the Joomla core, some are already in latest version of Joomla, others are more modern replacements for Joomla core libraries.
If you look at it in that context the name "Joomla Framework" still means the PHP libraries that are part of the Joomla core, of which some are available standalone through:
https://github.com/joomla-framework
How to integrate with Joomla through an external script
As far as I know there is not package or library in
http://github.com/joomla-framework that makes it easier to integrate with an existing Joomla installation. There is a revised Application package, but this doesn't help much for the existing Joomla core.
This brings you the following 3 options:
1. Boot the Joomla Cms
2. Use Joomla classes directly
3. Don't use any Joomla code
1. The best and safest solution to integrate with Joomla externally is to boot the Joomla Cms application. This way you are sure all the dependencies are properly loaded and everything works as it should be.
An example if our Joomlatools Console application bootstrapper. This is used by the console to bootstrap Joomla as a CLI application and allows you to use it from the CLI. It handles dependencies and bootstrapping for you. (Similar to the links you listed but for latest version of Joomla)
2. You could also choose an approach to use specific classes directly. This will quickly fail if you start to integrate with components, it will work if you need to call very specific API's that are uncoupled. However, there is a lot of coupling in the core to be able to do this safely.It might work if for example you only need the database layer, without any other dependencies.
3. In case you do not need to integrate with any of the Joomla classes or API's, for example as in your case you wish to merge to database tables you would decide to just use an external script that is completely custom, either written from scratch or using another framework or choice to help you.
About your problem