With the second example, I would use the plural. Since one doesn't really worry about a reader thinking that students have multiple noses, the plural is not really a problem.
Consider this sentence: The men were encouraged to bring their wife/wives to the closing session. There is no gender problem here, so put the sentence in the singular. Each man was encouraged to bring his wife to the closing session. Now we don't have to guess between men with multiple wives or a wife with multiple husbands.
Student or Learner