Q: Is it permissable to download a quran app because a phone is prone to falling out of ones hand and your phone is being used by other people all the time even if the app itself isn't open and do we need wudhu to download and use a quran app?
A: First of all, according to Ahmadi fiqh there is no prohibition to touch the mushaf in a state of minor ritual impurity (al-hadhath al-asghar), but only in a state of major ritual impurity (al-hadath al-akbar). Minor ritual impurity is the state, which requires wudu' before one can pray and major ritual impurity is the state, which requires ghusl before one can pray. So, one does not need to do wudu' before touching or even reciting from the mushaf.
As the digital version of the Qur'an is not tantamount to the mushaf, the rulings of the mushaf do not apply on it. Even if the mobile phone falls down, it does not correspond to the falling down of the mushaf. One can even touch the mobile phone with the Qur'an app open in it in a state of major ritual impurity.
Q: Wait this is ahmadi fiqh! Is it the opposite to non ahmadis?
A: The jumhur position (position of most scholars), and in this case the main position of the four prevalent madhahib of Sunni thought, is that wudu' is a requirement for touching the mushaf. The Ahmadi position is a minority opinion. Amongst others, some sahabah, like Ibn 'Abbas (ra), some tabi'un, like ash-Sha'abi (rh), ad-Dahhak (rh), al-Hakam ibn 'Utaybah (rh) and Hammad ibn Abi Sulayman (rh) were of this opinion and it is the main position of the Zahiri school of law.