Are we allowed to apply for a teacher? 

Edit:
Are all students gonna be in the same year? If so, which one?
Are all teacher positions open or just the ones you've written down? (Some are missing)
How canon will the wizarding world be? Did you research about the wizarding world in 1480 and Hogwarts' history? As well as each of the fantasy creatures you'll be using in this RP? Such as goblins. How much exactly do you rely on JK Rowling while creating this 1480 world?

If it's allowed to take a teacher for a character, I'd be interested in Care of Magical Creatures. Though that one is not listed on your main post. 

Will the teacher CS allow the person to choose a former Hogwarts house as well as a wand? Or shall that too be left blank for you to decide?
Is there a certain age range that you want the teachers to be? Maybe very young teachers don't appeal to you or too old ones don't. I don't know. 

Are we allowed to have connections/relationships with another person's character? That question especially goes for all who are Hogwarts year 2 and higher since then you'd know the people you go to school / work with already. Right?

It think that's all on questions I have so far.