Is the aforementioned situation considered a legitimate seclusion (khalwa shar'iyya)? Is the female employee's interaction with male students in the school library a matter of Shar'i embarrassment? What is the ruling on a Muslim woman uncovering her hair in front of a non-Muslim woman?

The forbidden seclusion (khalwa) is the gathering of a man and a woman where suspicion is not averted, and it has been prohibited.

What was mentioned in the question—regarding not being alone in the library, the presence of two doors, the presence of glass windows, and keeping the doors open—indicates that this interaction is not considered a forbidden seclusion.

As for a woman interacting with men at work to provide library services, if there is an alternative, it is safer (more precautionary) to leave it. However, if she needs to work, she must be cautious in her covering (hijab), not soften her speech, and avoid temptation.

As for a Muslim woman uncovering her hair in front of a non-Muslim woman, the preponderant opinion is that there is no harm in it.