Suggested answer:
(1) Examples of still and yet used as adverb(ials):
... when she was still a child
... he hadn't come back yet.

(2) In the following two examples still and yet have the meaning of "so far" / "up until now":
And they still haven 't rebuilt everything that the fighting destroyed.
...'but we haven't rebuilt it yet.'

(3) In the examples cited, still occurs medially, while yet occurs finally to convey similar meanings. The adverb(ials) cannot be moved in either context and still retain their meaning.

There are also instances where still and yet may convey similar meanings and occupy the same position in the sentence, e.g.:
There are still more challenges ahead of us...
And there were yet more that he would never be able to read...

Still another strategy is to change the probability that...
Yet another method is to keep the cow away...

(4) It is ambiguous because still in this position can function either as an adverb or an adjective:
At present there's still water in the tanks.

However, in the context it is most likely that still should be interpreted as an adverb.

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Read about the position of adverb(ial)s here.
Terminology: adjective, adverb, adverbial