Website updated - Tuition Website

I currently have a wordpress site made by another company learnalive.co.uk
I have a number of edits that need to be made to the site relatively simple
Changing some buttons
Adding some pages that are already created just copy and paste
New layout of the About Us Page to be more clearer using this example site: https://ting.com/
Optimise site properly for mobiles
Main Additional Function - Tutor Search Directory: We want to add the options for teachers to register themselves on our website and have a profile. This will only need to be so that students can view a description and if they pay then they can reveal the contact details of the teacher.
Students should also be able to leave feedback on the teachers profile.
Good example https://www.firsttutors.com/
We are happy to use existing wordpress functionality or other as advised when discussed.
We only need a basic functionality to begin with so we can create profiles for teachers and
So it needs a form to be completed by the teacher with payment button to complete registration
This should create a profile that students can search for by subject and location.
Payment access for the student to reveal the contact details.