Many people find this topic confusing, because we tend to bandy around USER and SCHEMA interchangeably, when they are in fact separate if related entities.
A schema is the collection of database objects owned by a user. When we create a user we create their schema at the same time. Initially their schema is empty.
It is easy to demonstrate that USER and SCHEMA are distinct, because we change the current schema in the session. This just means we can reference objects in another user's schema without prefixing them with the owner's name.
SQL> desc t1
Name Null? Type
----------------------------------------- -------- -------------
ID NUMBER
SQL> alter session set current_schema=APC
2 /
Session altered.
SQL> desc t1
ERROR:
ORA-04043: object t1 does not exist
SQL> sho user
USER is "X"
SQL>
In this case, either APC doesn't have a table called T1 or he hasn't granted it to X. The only way X can see her own table is to prefix it with her own name, or switch the current schema back to herself.
To answer your first question, the schema always has the same name as the user. So it is not possible for SCOTT to own schema X; schema X is owned by user X.
To answer your second question, it is impossible to create a schema without a user.
True, there is a CREATE SCHEMA command, but this requires the prior creation of the user. It is actually not creating a schema but creating several database objects. In effect it is more of a ADD OBJECTS TO SCHEMA command.
SQL> conn sys as sysdba
Enter password:
Connected.
SQL> create user x identified by x
2 default tablespace users quota 10m on users
3 /
User created.
SQL> grant create session, create table to x
2 /
Grant succeeded.
SQL> conn x/x
Connected.
SQL> create schema authorization x
2 create table t1 (id number)
3 create table t2 (id number)
4 /
Schema created.
SQL> select table_name from user_tables
2 /
TABLE_NAME
------------------------------
T1
T2
SQL>
The CREATE SCHEMA command is pretty limited: we can create tables, views and indexes, and grant privileges on objects. The advantage of it is simply that we can create several objects in a single transaction, so that all the creates are rolled back if one fails. This is not possible when we run each create statement separately.
Not sure what you're thinking off when you mention "function ID". It's not a standard piece of Oracle functionality.