Okay, here is how I interpret this structure. No particular rule, just use your common sense.
But has a meaning i.e. "Except" or "excluding".
In your first example:
All but the weakest plants survived the hot weather.
Simply, replace "but" with except. Now it stands as:
All except the weakest plants survived the hot weather.
Now consider this excellent example, I saw somewhere.
He is all but (.....anything; take a few pennies for example...) broke.
What does it mean? Substituting except for but once again, it means Except (a few pennies), he lost everything. Observe that, it does not mean, he lost everything. He has still left some pennies with him. So it is better to say He almost lost everything.
So in a nutshell,
He is all but a few pennies broke.
He has lost everything except a few pennies.
He has almost lost everything.
Now in the same way, if we apply the second rule to your second example, it becomes:
In some places, bus service has all but disappeared
Bus service has disappeared in some places, except a few buses.
Almost every bus has disappeared except a few buses.
Now use these two logic accordingly in your different examples.
(Hint: "It is all but impossible. " and "He was all but dead when we found him." In both the cases the meaning is "almost". Try to solve how.)