Is it permissible, in Islamic law, for a female student who wears the niqab to deliver speeches and lectures to male and female university students within the university campus for the purpose of da'wah (inviting to Islam), and should she continue doing so?

There is no legal impediment for a woman to invite men [to Islam] and teach them, provided that sedition is avoided and she adheres to the Sharia guidelines. The voice of a woman is not considered 'awrah (private/concealable) according to the most preponderant opinion. If a woman avoids sedition and commits no Sharia violation while delivering a speech, then there is no sin upon her, and she should not be blamed. However, if there are men available who can perform this task, then that is more preferable and safer.