Is Anesthesia Safe? - VeterinaryPartner.com - a VIN company!
This is a good overview on surgery.
I would not use halothane though (Iso or Sevo instead).
I would also prefer that a bile acids test be included in the preop blood work for Yorkies. A urinalysis and EKG preop can also be done if you want to be very cautious.
I would not leave an animal alone after surgery, so if they insist that the dog be monitored through the night, they need to let you transfer them to another hospital that is staffed 24/7.
Gas anesthesia (Iso or Sevo) should be used for maintenance but usually an injectable or IV drug is given first to give time to intubate.
Everytime anesthesia is used, there is a risk but it is still very safe. Sometimes you can do everything right and bad things happen and other times you will hear of animals dying under anesthesia when the proper protocol wasn't followed, so ask lots of questions and make sure somebody (usually a tech) is monitoring the animal while under because the vet can't do surgery and monitoring very well at the same time.