Yes, it is most preferable to face towards holy Kabah while praying from anywhere in the world. When Muhammad(PBUH) was sent as prophet in Mecca and in the early days, Muslims used to face towards Bait-Al-Maqdis mosque in Jerusalem which is different in direction in regards to holy Kabah. Then, after sometime, the qibla was changed by Allah towards holy Kabah. Look at Quranic chapter 2 for repetitive verses and its beauty in which Allah describes a lot about this change in direction.
Other than this, considering the following verse,
It is not righteousness that you turn your faces towards the East and the West, but righteous is the one who believes in Allah, and the Last Day, and the angels and the Book and the prophets, and gives away wealth out of love for Him to the near of kin and the orphans and the needy and the wayfarer and to those who ask and to set slaves free and keeps up prayer and pays the poor-rate; and the performers of their promise when they make a promise, and the patient in distress and affliction and in the time of conflict. These are they who are truthful; and these are they who keep their duty. Quran, Surah Baqra 2:177
I think the direction isn't a matter if you don't/can't find out the right direction towards kabah or if some explicit forces forbid you to pray. In this case, it may be valid that you pray regardless of facing qibla. Allah knows best.
Can you just fire off a few quick prayers without turning to face the Kaaba every time? For example a Christian might be sitting an exam; as they enter the exam room and take their seat they might close their eyes and pray a quick prayer asking for God to give them strength and Wisdom and Grace and bless their performance in this exam. Could a Muslim do this same thing? Or would they have to leave their seat and face Mecca for their prayer to be heard by God?
Regarding this, it is preferable only for Salaat (Salah/Salaat) prayer that you face qibla. Other than that, for mere supplications, he may sit anywhere (ex. exam hall) and start asking God for goodness in the activity he undertakes. He doesn't need to face towards qibla for this.