I am a Computer Science graduate with a focus on game development and a minor in Mathematics from Edinboro University of Pennsylvania. I am an expert in Unity3D and have recently released a game, Hippo Hop, on the Google Play Store. I am doing freelance work to support myself so I can continue work on my own projects.
I have a plan on how to convert questions from fixed to random, it may change based on how you are storing the current questions/answers but grabbing a random question and making sure it has not already been asked should be quick enough.
If you provide a 3D model with animations made (or a matching rig to the previous model) swapping that should be relatively simple.
When it comes to the state page replacement, I will draw you a mockup and you can tell me if that works for you or you want something different, we can go from there.
As for the video to get a correct answer, that should be simple enough but will again depend on which company you do ads through (Admobs, UnityAds, Chartboost, etc). As for keeping the app under 50mb and making it load faster, the easiest way to do that is to combine many 2D UI images into one "spritesheet". This makes for less files to load in and out of memory which makes things faster and less wasted space.
If you have any questions about my plan or the other minor updates you propose, feel free to contact me anytime. I am on the East Coast of the US so anytime between 9am EST and 12pm EST I should respond quickly