Series of questions about ER diagram and database?
Q1:  Why do you need a ternary relationship?  Test is a relationship between a patient and a doctor.  What is the third entity you need to specify in order to pin down a specific instance of a test.  I assume that a doctor can order more than one test for a given patient.
Q2:  They carry different information.  One of them is appropriate in any given situation, and the other does not carry the needed information.
Q3:  In the Chen ER model,  relationships are generally not given a primary key attribute.  Instances of the relationship may be identified by identifying each of the participants in the instance.
Q4: There is more than one way to skin a cat.
Q5: Make an entity weak if it can have no existence outside the context of the related strong entity.  Invoice detail line is a weak entity.  There will never be an invoice detail line without a corresponding invoice.
Q6:  There are hundreds of good textbooks to learn more about database design.  The ones by CJ Date are classics.  There a re a few good sources on EER,  but most good sources on ER will  incorporate EER concepts.  Here is a link to ternary relationships, but it repeats stuff you already know.  https://www.tutorialspoint.com/N-ary-Relationship-in-Database#:~:text=N-ary%20Relationship%20in%20Database%201%20Unary%20Relationship.%20When,a%20binary%20relationship.%20...%203%20Ternary%20Relationship.%20  the primary value to you is the terminology of N-ary relationships.  This should help you google.
You didn't ask this,  but you need to know it anyway.  There is a difference between analyzing the subject matter  (hospitals),  and designing a database to hold the relevant data.  People who do not understand the difference often end up producing the right solution to the wrong problem.