Asalamu 3alykum
As I understand this question is for brother Joseph I hope you don't mind me giving you some info to your questions.
For example, if one is out with friends and it is time to prayer but one does not know when they will be back home or in a place where they can pray how would one go about praying? Also, is one allowed to pray a car or while waiting in a store?
I take this situation to be in a country mainly consisting of non-Muslim population.
There are two exceptions that come to mind regarding your example.
64:16 So keep your duty to Allah as best ye can, and listen, and obey, and spend; that is better for your souls. And whoso is saved from his own greed, such are the successful.
2:239 And if ye go in fear, then (pray) standing or on horseback. And when ye are again in safety, remember Allah, as He hath taught you that which (heretofore) ye knew not.As you know the duty of prayers to believers are very important and are commanded to be observed at certain times.
Although one should always try to account for their prayers first around their daily life and understand and find a balance there is times or situations where prayers are difficult to perform because of the toils, journeys, and the attractions of this world especially in countries where prayers are not established publicly and prayers are seen to be at odds with their practices I find one should perform their prayer as best they can even in their car or standing or walking.
This does seem to conform to the rights given to believers in the verses above.
I was always taught that when you miss a pray when you come home to immediately pray it with the intention of praying a missed prayer, is this the correct/only way to go about prayers when unable to pray?
Although the Quran does not give any information regarding missed or late prayers and making up for missed prayers(which I find the silence of that information has much wisdom) there is nothing wrong with doing them as this will only show ones intention. As we know that God is the most forgiving and merciful, one would not doubt to imagine His acceptance if He wills.
God commanded prayers and I find if He had opened the door for missing prayers for us and performing them at later times, this would also give the excuses for people to miss prayers regularly. However the silence of information seems to be warranted and consistent with the command of prayers are to be observed at certain times in my humble opinion.
Also brother Joseph shares a time and experience he had with prayer.
Hope that helps Insha'Allah
A PERSONAL EXPERIENCE WITH PRAYER AT MADINAT AL-ZAHRA (AL ANDALUS) NEAR CORDOBA, SPAIN
http://quransmessage.com/articles/prayer%20at%20al-andalus%20FM3.htm