Does magento send automatic emails to confirm payments? (I'm using v1.6.2) This field is only for manual emails?
Yes Magento does send an email once an order reaches the 'processing' state. If you 'invoice' the order manually in Magento admin, you need to check the 'send email' checkbox to ensure the email is sent.
If the order is automatically sent into processing, then Magento will automatically send an email to the relevant email address.
If emails are not being sent or received then you will need to investigate whether the mailing service on the server is working. You can try the forgot password functionality as a test, make sure you check the spam folder.