As far as the question of Mahram is concerned, the underlying spirit is that you do not travel with a non mahram alone so that there is a danger of evil thoughts to mislead you, but with modern ways of travelling where you travel in public (airplanes), this question is not applicable. Before people used to travel individually on camel etc so a man and woman who are not related to each other and are out of public sight can think of many evil things, so to save from evil temptation women should not travel without mahram but now the situation is completely different.

There is a sound hadith recorded by Bukhari and attributed to ‘Uday Ibn Hatim, in which the Prophet (peace and blessings be upon him) predicts that “A day will come when a woman will travel from Hira to the Ka‘ba, fearing nothing but God alone.”