Guys, please advise me on what I should do?

I am working in one of the tech companies with a team of 3 members. Recently, we had a change of mentor and the incoming mentor doesnt seem to be very friendly.

I remembered the very first time he entered the office, he laid down some very weird rules.

1. We are to call him Dr. GX and not by his name. – Even though our company culture allows us to address each other like friends, he told us that this is for formality purpose and having an “advanced degree”, he deserves to be addressed that way relative to the commoners.

2. No mingering during working hours. – In the past, we have some “loudspeakers” in the company lighting up the stressful atmosphere with their jokes but now, things are different. Everytime he walks into the office, the atmosphere changes. He would give us the death glance and I remembered two days ago, one of those “loudspeakers” got scolded so hard by him to the extent that she almost cried. As a matter of fact, even her mentor dared not stand up for her.

3. No using of personal electronic devices during meeting, unless it is an emergency. – A day ago, I am pretty sure I was typing down notes on the laptop during the meeting and he told me” Hello, you emailing to your mum?” To protect my job, I didnt talk back to him and reluctantly apologised. (I had to use my brain to note down all his information subsequently)

Some of you may argue that these rules are reasonable and yes I agree, but not with the way he executes it. (I feel) that he might be suffering from some kind of Napolean Syndrome because he seems to have a tendency to find fault with the taller people in the company, be it guy or girl. On the other hand, when those average guy/girl commit serious mistakes, he will close one eye.

The thing is, even though this seems to be some sort of discrimination, he will always find ways to justify it (Basic manner, formality, coincidence etc). His English is so much better than us that there is no way we can defend ourselves.

I am thinking of blowing this matter up to the big boss, but there are rumours that he has a close connection with the HR people and this might backfire on me. Should I leave this toxic environment?