Hello there,
I'm working as cordova hybrid app developer from last 2 years and have experience working with various technologies like Ionic, Angularjs, JQuery, JavaScript, Php, Html5 and css3.
As per your requirement I can easily develop this app for you. Also I have noted that you don't need keyboard and user have to select latters from given list one after another.
Also I have done facebook, google+ login in so many apps and as I have well knowledge about php I also can create web services to store user information in mysql database.
Looking forward to work with you.
Thank you.