There are lots of good advice in the previous post's I will not repeat them.
It is difficult to estimate the degree of heel from the videos, people tend to estimate heeling to be more than it actually is. The only accurate way to determine it is to use a inclinometer I have one on my boat.
If I was to guess the heeling on the videos I would say something around 35 degrees.
I would not sail with this heeling if I had an inexperienced crewmember on board, my first priority would be to make sure that everyone on board are comfortable with the sailing – the purpose of the sailing is not to scare anyone away from sailing.
Most skippers tend to reduce sail to late and not to early..
The fact that the boat sailed with an instructor at the main sheet indicates to me that the skipper where a bit uncomfortable with the sail area the boat was flying under the wind conditions.
Normally the boat should be sailed by the students with the instructors guiding the students and look after the safety of boat and crew.
Please remember that most modern sailboats stop sailing effectively around 20 degrees of heeling, so there is now reason to sail with much heel.
Reducing sail area by reefing is (or should be) a easy procedure to perform, there are no excuse to sail with too much sail up.