Do you log in as your id with superpowers, the sysdba role, or the schema owner to run the sql?
You can not run the script by logging in as schema owner unless that schema user has appropriate privileges. You can login as superpower user and just set the current_schema=

Do you run from Toad or as a script (@c:\script) and do you spool your logs and if so how long do you keep them?
It is upto every individual. You can run through toad or sqlplus as well. You definately have to spool the logs. Retention period depends on request/criticality. You can make ur own folder to keep the logs

Do you request your developers to preface the objects in their scripts with the schema name?
Depends on the organization env. Generally developers repface the objects with schema name.

Do you have a change control process that you go through?
Sure...it has to be there.

Hope it answers your questions.

Regards and best of luck