Is it permissible to make up prayers due to the inability to maintain wudu' because of a chronic illness, the unavailability of places for wudu' outside one's residence in a non-Muslim country, and the difficulty of returning to university housing for each prayer? And is this considered missing prayers, to which the verse "Woe to those who pray but are heedless of their prayer" applies?

It is not permissible to deliberately delay the prayer beyond its prescribed time. If one has an excuse that allows for combining prayers, they should still be keen to perform them on time. If ablution is not possible, one should perform tayammum and pray. If one suffers from incontinence of gas, many scholars permit combining the prayers. In such a case, one should perform ablution after the prayer time begins and pray the obligatory prayer and voluntary prayers with that same ablution.