The mirrors in our studio are always covered when exams are going on, so I assume that they are not allowed for exams. So your teacher probably facing the class away to prepare them for the situation during an exam. Mirrors can be a great tool, but it's important to learn to feel where your body/body alignment is without a mirror, and not to get into a habit of dancing 'to a mirror'.
As to full vs. split sole, I am no expert, but it's my understanding that full soles help to strengthen your foot and so are often reccomended for young dancers in their first couple of years. It's rare to see professional dancers in full-soles as I think they tend to prefer the look/flexibility of split soles, but I have seen men practicing in full soles in order to work on their feet.
If you aren't going to be taking the exams and only there for one year, then I don't see any reason to switch shoes. I think it's more important to wear shoes that fit your feet & you are comfortable in, rather than to buy a new pair simply because they are required for exams you won't be taking. Of course, if you would be taking the exam or planning to study in the school long term then it would be a different issue.
For the record, I wear leather split soles, and have for all three year of my 'dance career'
) No real reason, but mostly because when I went shoe shopping, that's what was reccomended, and also because with medium-high, but stiff arches I was worried that I'd have a hard time keep full soles from flipping off my heels, elastics or no elastics.
To be honest, I've never really understood the strict 'uniform' requirements for RAD - perhaps someone could explain why they are so strict... Does the standarization lower prices? Or just line the pockets of the few 'RAD' approved companies? Many (most?) non-RAD schools that know about do have uniform requirements, but suggest rather than require certain brands and allow some leeway for different body-types.