What is the ruling on studying at a coeducational university when affordable non-mixed universities are unavailable, and there are Sharia-compliant and committed regulations in place?

If there is a distinction in the seating arrangements for male and female students in the classroom, this does not constitute forbidden mixing, and there is no harm in studying at this university.

As for the presence of the car owner's brother with you both, his presence negates khalwa (unlawful seclusion) if temptation is secure, because the preponderant opinion is that the presence of two trustworthy women with a man negates khalwa.