Is it stable to run Drupal 7.8 on php 5.3.8? I would like to make use of php 5.3.x built-in fastcgi functionality and therefore I would like to migrate from php 5.2.x to php 5.3.8. 

Is it stable to run Drupal 7.8 on php 5.3.8 ?
Yes. In fact, it is recommended to do so.