“ORA-00942: table or view does not exist” when deleting from a very real table in the user’s schema

The error you're getting indicates that a query is trying to reference an object that doesn't exist or that the user doesn't have access to. If you started getting it a week ago and weren't getting it before that, something changed a week ago so that an object was dropped, a privilege was revoked, or a SQL statement was added that references an invalid object. It is unlikely that upgrading the database would resolve the error.

Can you determine the SQL statement that your application is issuing when it receives this error? If not, can you add additional logging so that you can determine what statement is generating the error? If your application doesn't log the SQL statements it generates, you could create a SERVERERROR trigger (based on this trigger code). Obviously, you would probably want to log more than just the SQL statement.

create table stmt_err_log (
  sql_stmt varchar2(1000)
);

 CREATE OR REPLACE TRIGGER after_error
  AFTER SERVERERROR ON DATABASE
  DECLARE
  pragma autonomous_transaction;
  id NUMBER;
  sql_text ORA_NAME_LIST_T;
  v_stmt CLOB;
  n NUMBER;
 BEGIN
  n := ora_sql_txt(sql_text);
  --
  IF n >= 1
  THEN
    FOR i IN 1..n LOOP
      v_stmt := v_stmt || sql_text(i);
    END LOOP;
  END IF;
  --
  FOR n IN 1..ora_server_error_depth LOOP
   IF ora_server_error(n) = '942'
   THEN
     insert into scott.stmt_err_log( sql_stmt )
       values( v_stmt );
     commit;
   END IF;
 END LOOP;
  --
 END after_error;

You created the table in the SYS schema (which you should never, ever do. Really, never).

When you log in as teacher1 any statement looks for objects in that schema. But there is no TEACHER1.INSTRUCTORS table, because the real name is SYS.INSTRUCTORS (did I mention what a bad idea it is to create objects in the SYS schema?).

You need to run select * from sys.instructors to get access to that table. If you don't want to prefix the table name with the schema, create a synonym in the teacher1 schema:

create synonym teacher1.instructors for sys.instructors;

Then teacher1 can access the table from the SYS schema without fully qualifying it.

Again: stop using the SYS or SYSTEM account for anything that is not DBA stuff. Use a regular account for that.