User Registration Form

I have an Avada theme and I would like to create with the theme a friendly page where the user can enter a lottery ticket to see if it’s a winning ticket or not. Upon entering the ticket number in a text field and clicking “go”, the user will be prompt to register to the site where one of the custom fields will be the ticket number that should be filled out automatically since it was entered before registering. After the user registered, the ticket number will be checked on the database to see if the number entered exists or not. Every week more numbers will be added to the database.
What I have thought using is the WordPress plugin User Profiles Made Easy for the front-end user login/registration. Now where I am stuck is if there’s any solution out there where I can put a custom PHP script that will check if the number entered exists in the database or not. If I have to do it manually, how and where can I put that code in the plugin that I mentioned (or a similar plugin). Additionally, how can I access the database and create a table with the numbers that will be added weekly (an expandable database)? I am confused on how to interact with plugins and themes to create the visuals and registration form and my own code (if I have to). Any ideas or suggestions?