In ordinary circumstances,
none of the above is true FWIW.
It's very rare that an entire hand is called off and redealt because of dealer error, especially if there's been any betting action. There are methods for correcting just about any conceivable dealer error with minimal impact on the outcome of the hand.
I've seen dealers make multiple errors that required floor intervention and still be left in the game until their rotation was up, and while they probably will get a talking to if they're prone to making these kind of mistakes a lot, a minor one-off error like burning two cards isn't likely to get anyone chewed out or fired.
Dealers are human. Mistakes can be corrected. Take a deep breath