Logon trigger questions

I am using Oracle 9.2.0.5 on HP NIX 11i but question is general.

I am developing a logon trigger for running some alter session commands. However, if there is any error in execution of logon trigger, I will still like logon to succeed. In addition, I will like record Oracle error message in alert.log.

CREATE OR REPLACE TRIGGER my_logon AFTER LOGON ON database BEGIN

• call function to use outline in some category my_outlnfun; When others
  • write error message to alert log
  • what happens if there is error in writing to alert log (do I need
  • to put error message to alert log in another begin block?

END;

1. Will above code do what I want?
2. What is Oracle function to write to alert log?
3. I do not know when trigger becomes invalidated instead of giving error? If trigger is invalidated, is only fix is to conn / as sysdba and disable it.