Can i pair multivalued attribute with an entity?
Yes, you can. 

You could create a table for Diseases:

TABLE disease
-------------
disease.id (PK)
disease.name 


Then you can model Diagnosis (note that's a junction table) this way:

TABLE diagnosis
---------------
diagnosis.id (PK)
diagnosis.date
diagnosis.doctor_id (FK)
diagnosis.patient_id (FK)
diagnosis.disease_id (FK)


So you can add a Disease to an Investigation:

TABLE investigation
-------------------
investigation.id (PK)
investigation.type
investigation.title
investigation.description
investigation.disease_id (FK) 


And finally, here's the table for Testing:

TABLE testing
-------------
testing.id (PK)
testing.date
testing.investigation_id (FK)
testing.patient_id (FK)


The Testing can as well be included as a field in Investigation instead of having its own table, unless the exercise requires it.

Then there are the tables for Doctor and Patient which you already modeled.

This is the description of the tables, from it you can easily create the ER diagram, remembering that a FK on a table connects to the PK on another table.