Can I have multiple nested forms within the same fieldset?
You can have both buttons in the same form. Inside the form's #submit handler (or each button's separate #submit handler), based on which button has been used to submit the form, you can either save the data, or do a drupal_http_request() to execute the external script.

Your form would include buttons roughly like this:

'save' =&gt; array(
  '#type' =&gt; 'submit',
  '#value' =&gt; t('Save'),
  '#submit' =&gt; array('save_function_name'),
),
'process' =&gt; array(
  '#type' =&gt; 'submit,
  '#value' =&gt; t('Process'),
  '#submit' =&gt; array('process_function_name'),
)


Then, the two functions save_function_name() and process_function_name() would do the job.