Do I need to create indexes on foreign keys on Oracle?

The foreign key constraint alone does not provide the index on Oracle - one must (and should) be created.

Just for more info: Oracle doesn't create an index automatically (as it does for unique constraints) because (a) it is not required to enforce the constraint, and (b) in some cases you don't need one.

Most of the time, however, you will want to create an index (in fact, in Oracle Apex there's a report of "unindexed foreign keys").

Whenever the application needs to be able to delete a row in the parent table, or update the PK value (which is rarer), the DML will suffer if no index exists, because it will have to lock the entire child table.

A case where I usually choose not to add an index is where the FK is to a "static data" table that defines the domain of a column (e.g. a table of status codes), where updates and deletes on the parent table are never done directly by the application. However, if adding an index on the column gives benefits to important queries in the application, then the index will still be a good idea.

Creating a foreign key does not automatically create an index on A.B_ID. So it would generally make sense from a query performance perspective to create a separate index on A.B_ID.

If you ever delete rows in B, you definitely want A.B_ID to be indexed. Otherwise, Oracle will have to do a full table scan on A every time you delete a row from B to make sure that there are no orphaned records (depending on the Oracle version, there may be additional locking implications as well, but those are diminished in more recent Oracle versions).