Due to my busy schedule lately I have missed or said prayers late. I am a university student, I work, and my wife and we are expecting a child soon. I also have to transport her to and from school and work as we only have one car. Often the only prayers I make on time are Fajr and Isha. Is it okay for me to say prayers late, as I have not found a place to pray at my workplace or at the university? And is there anything I can do to make up for missed prayers?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

You are obliged to perform the prayers in their fixed times. It is forbidden to delay them till the fixed time ends whether one is at university or any other place.
If you try to perform the prayers on their fixed times surely you will find the time and the place. Always bear in mind that the Prophet (Sallallahu Alaihi wa Sallam) said: "The earth has been made for me (and for my followers) a place for offering Salat (prayer) and a thing to purify (perform Tayammum), therefore anyone of my followers can offer Salat wherever he is, at the time of a Salat" .
As for the prayers you missed then and still have not offered yet, you have to make them immediately after knowing the rulings. May Allah help you.
As for how to make up missed prayers please read the Fatwa: 83818.
Allah knows best.