Is it necessary to refrain from speaking to or looking at female students or teachers who are immodestly dressed in mixed-gender schools, especially when there is a need to learn or answer teachers' questions?

The default rule is that it is impermissible to study in mixed-gender universities, except out of necessity, provided that there is safety from temptation and adherence to Islamic regulations. As for speaking with immodestly dressed women, one must consider the benefit and harm involved. If there is a benefit, such as da'wah (inviting to Islam) or a need, then it is permissible; otherwise, it is better to avoid it. It is obligatory to fulfill the duty of inviting to Allah, enjoining good, and forbidding evil to the best of one's ability.