You need to create a template override for the article view - default.php template file.
Layout Overrides in Joomla.
How to override the output of Joomla core
Understanding Output Overrides
So there you can create a "modal button" for the register link, to open the registration view inside a modal window.
This blog post explains how to create modals ...
When an article is saved, JTableContent (\libraries\legacy\table\content.php) saves anything before the readmore tag in the introtext field and anything after in the fulltext field of the content table. The tag itself it not saved in the database.
You can see the structure of that table here:
The code Joomla uses to ...
At the time we don't have an automatic feature for this in the core, you can do this manually by adding one by one in your content or you can add a custom code via override for the blog layout.
Also you can try with one extension in order to automate more this process, here you have two possible options:
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