A. First of all after birth a dog can have vaginal discharges for a few weeks, that would explain the licking.
Because she gave birth to a dead puppy something might be wrong with her uterus, possibly an infection has already started. If she develops pyometra (uterine infection) this is a very severe condition.
I recommend getting her spayed ASAP, bare in mind you might be surcharged if there is an infection as the procedure is much more complicated.
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