The login and signup boxes of Universal Login cannot be split up like you describe, but you can be directed to either one with certain params. Here is a relevant topic:
I am not sure I understand what you mean here. Universal Login certainly works out of the box, but obviously cannot conform to every single use-case out there. For this exact reason we provide API endpoints for full control and customization.
As far as conversion goes, a custom signup page is likely to provide the most tailored experience for your specific customer base if that is your main concern. For example, we use a custom signup experience.
I am not very familiar with shortcode, which seems like a wordpress-specific feature. If I am missing something regarding that please let me know.