Does Primary key in Dimension table have to be part of the Primary key in the Fact table?

It is a good practice because it helps ensure that all your facts reference existing dimension members, and may improve performance in some DBMS, but as with any other design/approach it is not mandatory.

Composite keys for fact tables are actually a recommended practice by Kimball's dimensional modelling methodology, namely because:

In most environments this composite key will suffice as the primary key to the fact table. There is typically no advantage of assigning a surrogate key to the fact rows at a logical level because we have already defined what makes a fact table row unique.