Wow! that’s some observation.

Addressing your points

1. I did think of having a direct integration of a student’s phone number to the contact list, but I had decided that the find people page will only provide the name, department, room number and email of a student. This is because I was not sure about the privacy concerns of people (especially the female students) if their phone number was available to everyone. I guess a user research specific to this feature would be helpful to decide.
2. You are right about the phone icon indicating to call someone. It does have a calling function. I have not shown any phone numbers in the page, one can directly call just by looking at the name of the person . I feel phone numbers work like an address. The primary function is to have a conversation and not showing the phone number does not obstruct that. The case where a person has two phone numbers would be where it would be necessary to show the numbers. Regarding the icons. Just the general search icon makes it ambiguous, Users might not know what they possibly could search for, in that tab. That is the reason I used a person and a magnifying glass both in a single icon (Makes it clearer).
3. The hamburger menu has 3 options : ID card, Dark mode and Sign Out! I hope this doesn’t make it so ambiguous.

All the points you mentioned are legit concerns and I think things will get clearer once I get the user testing results and try out A/B testing as well to see what works the best.