Is a girl's prayer valid if she experiences discharge—without desire—after performing ablution (wudu') and before praying, and she does not perform ablution for the subsequent prayer, given the unavailability of a clean place for ablution at the university? And is it permissible for her to perform tayammum (dry ablution) in this situation?

If the discharge of secretions is merely a doubt, then do not pay attention to it. But if you are certain of their discharge, then you must perform ablution (wudu') for it, because it nullifies ablution. Tayammum (definition) (dry ablution) is not sufficient as long as you are able to perform wudu'. Also, avoiding impurity is possible, and you can perform ablution in another place. What you mentioned is not an excuse to abandon ablution. You can combine two prayers that share a time if performing ablution becomes difficult for you.