Hook into node operation from theme template.php? I have made a new content type in Drupal 7 in Drupal Admin (not via module). What I want to do is to add a Hook on the insert and update operation. How can this be done when my node type is not created by a module?

Can this be done at all?
You want to create a custom module. Note that nothing stops you from creating content types through the user interface, it is in fact the suggested way to do so nowadays with fields and stuff (instead of using hook_node_info())

Node API Hooks contains an overview of all hooks that can be used to interact with nodes at different events like create, view, delete..