Is it permissible to combine prayers due to circumstances that prevent ritual purity and prayer on time, such as being in transportation or the inability to pray in the street? And does this apply to my sister combining the Dhuhr and Asr prayers with an early combination due to an exam?

A Muslim must perform the prayer at its legally prescribed time, as Allah Almighty says: "Indeed, prayer has been decreed upon the believers a book [due at] fixed times." It is permissible to combine two prayers while in residence (not traveling) out of necessity, provided it is not done habitually. This is based on the hadith (definition) narrated by Ibn Abbas in Sahih (definition) Muslim that the Prophet (peace be upon him) combined two prayers in Medina without fear or rain, intending thereby not to cause hardship to his Ummah. A group of imams, such as Ibn Sirin, Ashhab, and Ibn al-Mundhir, adopted this view.