How much is keeping an autopsy private going to cost Mrs. Stack?
If Mrs. Hunter decides to drop the lawsuit will the autopsy be available to the public? Do they need to see the wrongful death case through to the end to keep the autopsy private?
Ripe for speculation.
How much is keeping an autopsy private going to cost Mrs. Stack?
It's entirely out of the hands of Mrs. Stack with respect to the autopsy results becoming public. The fact of the matter is that they are public records as they are records and evidence in a law enforcement investigation.
If Mrs. Hunter decides to drop the lawsuit will the autopsy be available to the public?
They'll be made available - at some point (sooner rather than later) - irrespective of the outcome of this suit.
Do they need to see the wrongful death case through to the end to keep the autopsy private?
The chances of these records remaining "private" are slim and none. Any person, to include countless media organizations, will be able to sue for these records under whatever the name of the Texas sunshine law is.