Is it permissible for a 17-year-old male student to coordinate with his paternal uncle's daughter, who is one year his senior, and for them to go together to study due to their sharing the same route?

Your paternal uncle's daughter is a non-mahram, and she must be treated as such. Accompanying her to any place is a pretext for temptation, and her riding with you in the car constitutes khalwa (private seclusion), because some contemporary scholars have issued a fatwa that a woman riding alone with a driver is khalwa. Therefore, the causes of temptation must be avoided.