First, I want introduce myself, I am Mercedes, I have more than three year doing native android applications, any field where I dabbled are financial with mobile banking applications, marketing with mobile loyalty programs.
I understand that you need an application where users answer true/false quizzes. For that need development, first the Backend, in there we will management the list of questions, the list of users and their highscores, additional we need to place a section to set the time available to answer a question and the last seconds (when the question is colored in red), according to the description the system just will have one administrator user. Apart from this in the backend I've included when developing web services (in Restful) for register of users (by facebook or email and password), login (in the same way than the register), obtaining questions and the configure time for answer it, and send the highscore to the backend. Second the android application, we need to permit at the user register with facebook or email and password, then the login, after that start a round of questions, here we will show to the user the available time and when the time will be 10 seconds put the question in red, give the opportunity to skip the question and not count this one for the highscore, reproduce sounds and finally give the option to share on facebook the highscore and submit that score to the backend, finally the user can start a new question's round.
Any doubt contact me