Hello,
First of all, let me start with the obvious..to me... you don't have an sql expert in your company....
the database you provided would work, but it's awfully designed... i would use my own system for login (fully compliant with NIST SP 800-132) that means in the remote chance a hacker gets access user passwords are close to impossible to crack.
Your view, of one php file per page is ok.. badly educated programmers especially like it, but i propose my own framework. you don't have to know anything about it, all the controller files will be one file per group of actions, but it will be secure, fast and easier to maintain.
your question / aswer table is fixed and if you want to add another question u're screwed. My solution would be to redesign it so you can have 1000000 questios if needed. I would also store 'not frequetly searched' data in JSON format to save some DB overhead.
And depending on the chosen DB schema I would add indexes and I need to mention that I know about 'explain' (most freelancers here do not)...
OR
I can do the project for $800 in exactly the way you described it. with one php file per action, with exactly your DB. just like any other freelancer here, but more secure (using PDO, not mysqli or even worse mysql) and lighter on the server. ( i'm a performance freak and I optimize everything - my hobby).
If you have any questions, please ask.
Sorry about the long message.
Regards,
George