How to disable Ubercart order mail notification? Everytime a customer places an order, the store owner gets an email with the order invoice. Where can I disable this? (the webshop is still in production)

Also, is it possible to set up a conditional to only send an e-mail when the customer has paid? (right now paypal payments works)
You can disable the Rule (Configuration -> Workflow -> Rule):
E-mail admin checkout notification.

About the second question, you can customize the Rule:
E-mail an order update notification 
to email the store owner when the order changes status AND when the status is equal to "Payment received"

Hope this helps