Which one is created first? Database or Instance

Your kernel parameters need modifying.

Edit /etc/sysctl.conf and ensure the following lines are present:

kernel.shmall = 18350080
kernel.shmmax = 75161927680
kernel.shmmni = 4096
kernel.sem = 250 32000 100 128

Then reboot the machine.

You could encapsulate the logic into the packages themselves:

SQL> CREATE OR REPLACE PACKAGE pkg IS
  2     g_context VARCHAR2(30);
  3     FUNCTION  get_ctx(p_variable VARCHAR2) RETURN VARCHAR2;
  4     -- set_ctx may be private of course
  5     PROCEDURE set_ctx(p_variable VARCHAR2, p_value VARCHAR2);
  6  END;
  7  /

Package created

SQL> CREATE OR REPLACE PACKAGE BODY pkg IS
  2  
  3     FUNCTION  get_ctx(p_variable VARCHAR2) RETURN VARCHAR2 IS
  4     BEGIN
  5        RETURN sys_context(g_context, p_variable);
  6     END get_ctx;
  7  
  8     PROCEDURE set_ctx(p_variable VARCHAR2, p_value VARCHAR2) IS
  9     BEGIN
 10        dbms_session.set_context(g_context, p_variable, p_value);
 11     END set_ctx;
 12  
 13  -- set ctx dynamically
 14  BEGIN
 15     g_context := 'MYCTX_'||sys_context('userenv', 'current_schema');
 16  END;
 17  /

Package body created

Let's create the context and call it :

SQL> BEGIN
  2     EXECUTE IMMEDIATE 'CREATE CONTEXT ' || pkg.g_context || ' USING PKG';
  3  END;
  4  /

PL/SQL procedure successfully completed

SQL> exec pkg.set_ctx ('a', '123');

PL/SQL procedure successfully completed

SQL> select pkg.get_ctx('a') from dual;

PKG.GET_CTX('A')
--------------------------------------------------------------------------------
123