Wordpress Database PHP, AJAX Question

Hello,
I am a Wordpress newbie but have experience in PHP, MySQL, AJAX programming.  Most of my experience is in back end processing.  I know and am comfortable with MySQL queries, AJAX, some Javascript, PHPm XML, JSON.  I know how to create simple forms and using _GET, _POST processing can handle making requests to the MySQL DB, processing the XML responses (in the case of AJAX).  A simple example is in the case of a user login situation where using AJAX I can take the user email address and passwords submitted in a simple HTML form, pass those as params via AJAX to a PHP server processing script which queries the MySQL table for the result.  Then based on result allows user to log in or not and redirects user to a page for example if user passes authentication.

My difficulty is in understanding how to perform this very basic functionality in Wordpress.  I have used form builders like Ninja Forms to graphically build a form creating a form with text fields for user email and password and also a submit button.  I was able to have this form successfully displayed on my Wordpress site and performed a test on this form.  The form submission was successful and the data from the form scenario results in an email being sent and/or being recorded in the "Submissions" area of the forms tab within the wp-admin  dashboard.

What I can't figure out is:
1) How can I grab that information (user email address, password) programmatically so I can query a non Wordpress table.
2) How do I integrate custom PHP pages into my Wordpress site.  I used a plug-in called "Insert PHP" where I use special delimiters to include an actual .php file in a page created in the wp-admin dashboard but this seems like a clunky solution.  I read up on Wordpress tutorials and I understand that posts, pages created in the wp-admin dashboard are not actual files so I can't just go to the source code of those posts/pages and customize them.  I also read that I just can't go into the Wordpress file directories to hack Wordpress core files.  I also read that for some complex functionality, it may be required to write a plug-in myself to handle more complex situations.  However I think I am missing something basic as I wouldn't think getting some data out of a form and querying a MySQL DB should be that hard to necessitate writing a plug-in.

Thanks in advance for help.
XL2015Asked:
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Jason C. LevineDon't talk to me.Commented:
1) Use the wp_signon() function to process credentials.

https://codex.wordpress.org/Function_Reference/wp_signon

I read up on Wordpress tutorials and I understand that posts, pages created in the wp-admin dashboard are not actual files so I can't just go to the source code of those posts/pages and customize them

2) Actually, they kind of are.  WordPress has a template system at the theme level and you can alter the base template or create your own to handle things.

https://codex.wordpress.org/Pages#Page_Templates

but depending on what exactly you want to do and how available you want it to be, you may indeed need to write a plugin or add the functionality to the theme's functions.php file.  One of the things you will learn by reading the WordPress Codex (https://codex.wordpress.org/) is which functions fire when and that can affect how your custom scripts work.

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XL2015Author Commented:
Sorry for delayed response as we had few emergencies to attend.

We have put the project on hold but we feel the same that we may have to write our own plugin to perform the task.  Thank you for the suggestion
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