Skip Payment Method - skip payment method means that if you e.g. want to give users something without payment, you can automatically hide the payment form when it meets the criteria (e.g. the order amount is zero). And yes, if there is no payment, it cannot change the status (as if there is) by payment method.
Hmmm, it is really hard to say what can be wrong there. If there is some problem on server or if there are always different conditions under each the sending work or does not workSometimes email is sent with download link, sometimes not...
Jan