Help integrating WordPress and a separate PHP Framework.

Greetings All,

Purpose: WordPress Website running a magazine theme with a social network aspect. WordPress’s only operation here is to provide the content for the user base to see.

Current Framework:
a). Directory holding: WordPress with a magazine theme for content, posts, articles.
-Two buttons on all WordPress pages (Login + Join) leading to respective (blank) pages.

b). Directory holding: PHP Login & Register system built from scratch links to a distinct MySQL db with users, friend requests, followers, etc.

Procedure:
-When user session begins, user profile data is echoed to all of wordpress pages. Login
and sign up buttons disappear. The rest can be handled as far as search results and
comment functionality.

Current Thoughts:
-Extract all html/css from wordpress files with shell scripting or perl to retain the
responsive style.

-While it retains links that can be changed to integrate this into the
other login system, I am aware that I forfeit control of simply editing an article/page—I
have a solution built from scratch to handle this as well.

Ideally:
-No signing up to the site where I enter my admin username and password (security).
-No plugins unless absolutely necessary (something that cannot be coded)
-Absolutely No Buddypress (its security is weak)

Concerns:
-Is there a cleaner way to achieve this?
-What are the different ways to achieve this?
-Am I thinking about this sufficiently based on what I have here?
-If you wanted to design the same, where would you begin your editing?
-Are there clear (not walls of text) examples of this type of framework? If so, where?