Are ER diagrams independent of a DBMS? When modelling a database, does the ER diagram depend on the DBMS used to implement the said ER?
When the ER (Entity-Relationship) model was devised in the 1970s, it was specifically intended to be implementation neutral (sometimes called "implementation agnostic").  The relational model, by contrast, was tilted towards a relational design and implementation.  

In classical three stage methodology, an ER model is devised to capture the data analysis of the subject matter.  You could implement the database as relational, or OODB, or unstructured, or whatever. This is called the conceptual model. 

The next model is a relational model, and captures the logical design.  This is tilted towards a class of Relational DBMS products that includes Oracle, SQL Server, and many others.  This is called the logical model.

The third model is a detailed model of the proposed database, and captures features that are DBMS specific, like indexes, and table spaces.  This is called the physical model.

Very often the logical and physical models are merged together, because the DBMS has already been chosen, and they are both design models.