All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
With regard to the first two questions, there is nothing wrong with doing what is mentioned in them if the following conditions are met:
First, the school's bylaws and regulations must allow it.
Second, there should be no forbidden seclusion involved. Scholars defined the forbidden seclusion as a man being alone with a non-Mahram woman in a place where no third person would enter.
Third, there should be no fear of Fitnah (temptation) and its causes such as not wearing the Islamic Hijab, over-friendliness, laughter, and so on.
If these conditions are met, there is nothing wrong with it, as we have said, and if there is no need for being alone with a non-Mahram woman, it should be avoided in any case because it is more prudent and safer in terms of clearing one’s liability and distancing oneself from Fitnah and its causes.
If any of these conditions are not met, such seclusion is deemed forbidden and the doer bears sin for it.
In order to be safe from potential Fitnah, some jurists even held that it is disliked for a man to lead a non-Mahram woman in prayer. An-Nawawi said in Al-Muhaddhab: “It is disliked for a man to lead a non-mahram woman in prayer. It was narrated that the Prophet said: “There is absolutely no man who stays in seclusion with a woman except that the devil is their third companion.” [Ahmad and At-Tirmithi]
You should look for another place to pray, and if you cannot find any, there is nothing wrong with praying in this place, provided that you leave as soon as you perform the prayer.
Allah knows best.