Never knew that this is possible until I read it today. However I have a question, what if I have created two transactions, one with fees and one without fees? I send 1 btc to the same address two times but with only different fees. Is it possible that the two tx be confirmed at the same time if I only have 1btc?
No, only one can be confirmed, and the other will become invalid at the same time.
Even if they get confirmed at the exact same time? Which transaction will be flagged as invalid by the network? The one with the fees or the one without fees?