1) What would Donald Shimoda tell me, if he were sitting here under the wing tonight, if he knew I had not found her yet?
Although that example sentence is an excerpt from prose that is past-tense narrative fiction, the example sentence is the narrator's direct thoughts -- and so, the grammar related to this sentence is the same as would be if we had put quotes around that sentence and treated it as dialogue.
Keeping that in mind, then we can see that the two "if" clauses are involved in remote conditional(s). So, let us first look at an open conditional that could correspond to your example sentence:
- 2) What will Donald Shimoda tell me, if he is sitting here under the wing tonight, if he knows (that) I have not found her yet? -- [open conditional]
Notice that in the open conditional version (#2), that it uses the present-tense verbs "will" and "is" and "knows" instead of the past-tense verbs or irrealis "were" verb in your original version (#1).
In the open conditional, the speaker doesn't give an opinion as to what he thinks is the likelihood of the "if" clauses being true or false -- he is "open-minded" as to that.
But in the remote conditional, the speaker does have an opinion, and his opinion is that he finds it doubtful (or possibly even counter-factual) that the "if" clauses could be actually true -- thus, the modally remote use of the past-tense verbs. So, in your original version (#1):
- 1) What would Donald Shimoda tell me, if he were sitting here under the wing tonight, if he knew (that) I had not found her yet? -- [remote conditional]
that means that the narrator (speaker) thinks it doubtful (or impossible) for Shimoda to be sitting here under the wing tonight, and thinks it doubtful that Shimoda would know that the narrator hadn't found her yet.
Note that in the remote conditional version (#1) the two situations being described in the "if" clauses are still in the present time sphere, just like they were in the open conditional version (#2). That is, the past-tense verb "knew" is not being used for past time use. (Also, be aware that the past-tense verb "was" could also be used here in your original example, instead of the irrealis "were".)
Grammar-wise: Notice that in the remote conditional version (#1), that it uses the past-tense verbs "would" and "knew" and the irrealis "were" verb to show the speaker's opinion. Also notice that the "have" has been replaced with a backshift "had" -- which can be done here because the subordinate clause ("(that) I have not found her yet") has a superordinate clause that is headed by a past-tense verb ("knew"). This means that the past-perfect in that subordinate clause does not involve two past-times, but only one -- for the "had" is being used for modal remoteness, not for past time use.
To answer your first question: Since the "yet" seems acceptable in the present-perfect construction in the open conditional version (#2), that means that it seems to also be acceptable in the past-perfect construction (the original version #1).
To answer your second question: As to the "second if conditional", you could probably consider it either embedded within the first conditional "if" construction or consider the two "if" clauses to be in "and" coordination. There probably isn't much, if any, pragmatic difference between the two interpretations. (Though, syntactically, your teacher might want it to be parsed in a certain way.)