Tables:
Students
Professors
Entries (there’s no physical table intry in the database for entries yet, this table is on the front-end, so it is probably composed from multiple helper tables if we need them. Just need to create valid erd)
Preambula:
One student can have an association to many professors
One professor can have an association to many students
One entry can have 0,1 or more Students or professors in it.
Professor is required to be associated with one or more students
Student is not required to have an association with any professor
It should be more like this (front-end entry table):

Any professor in this table must have an associated name in the table.( For example Wandy is associated to Alex)
It is not required for student (but possible) to have associated professors in this table
One row (for example Linda (Student), Kelly (Professor),Victor (Professor))
Cannot be associated between each other in any manner.
But it is absolutely fine if Linda associated with David.
The problem is that I do not quite understand how one column can have ids of different tables (And those are multiple!) And do not quite understand how to build valid erd for that.
I will answer any additional questions you need. Thanks a lot!
If you simply want an association between Students and Professors – just make a many-to-many relationship in ERD. In logical (relational) schema it will make an intermediate table with foreign keys to Student and Professor tables.
But from your example it looks like you need to design the DB for your “PeopleEntries”, which is not straightforward. ERD seems to have the following entities:
name)
LoveDogs, LoveAnts)
Relationships (considering people cannot appear in entries more than once):
Relational schema would contain tables (foreign keys according to erd relationships):
FK)
LoveAnts)
ProfessorID FK)
I don’t know how to implement the constraint, disallowing association between people from the same entry, on conceptual level (ER-diagram). On physical level you can implement the logic in triggers or update procedures to check this.