All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, may Allaah reward you for being keen on observing the religious rulings, so may Allaah increase your piety and guidance, and enable your parents to embrace Islam. We advise you to continue calling them to Islam and continue to be kind and dutiful to them hoping that Allaah will open their heart to Eemaan (faith). For more benefit, please refer to Fataawa 85180 and 83566.
You should know that it is not a condition to have a Mahram in order to reside in the place of your residence, but you are obliged to reside in a safe place.
As regards studying in a mixed university, then this is not permissible if the two sexes are not separated, but if the two sexes are separated, then this is permissible. If we presume that the two sexes are not separated and you are in need of this study as it might be understood from the question, then if you are able to avoid the reasons of temptation and be present in the university according to the need only, and then you leave the university, we hope that it is permissible to continue the studies.
However, it is not permissible to travel without a Mahram. Therefore, you may be patient until you finish the studies and then you may travel afterwards. If you are in need for the studies, then some scholars are of the view that a safe company serves as a Mahram for a woman. So, you may travel on a safe route in a direct trip, and you continue your studies until you finish. Nonetheless, if you are able to marry a Muslim man in that country, then this might be better so that he would help you and accompany you when you travel to your family.
Finally, it should be noted here that it is permissible for a Muslim woman to propose herself to a pious man in order to marry him. In this regard, you may seek the help of some pious female friends of yours. In case you do not have a Muslim guardian to marry you off, then you may appoint a Muslim man to marry you off; for more benefit, please refer to Fataawa 88488 and 82471.
Allaah Knows best.