Learn English – what book to read & which book to read

That's a good question.

The answer, I think, is that not only acts as a unit. I can't think of another adverb which can take not in this way.*

The regular form I didn't only lose all my money is also possible.

*Constructions with not + adverb are common when there is no verb, as in "Do you always go that way?" "Not always"; or "He finished the job, but not quickly". But when there is a verb, the negative normally goes to the verb in the usually way "I don't always go that way"; "He didn't finish quickly".

Edit: I have thought of one more example: not infrequently. But neither often nor frequently works this way.

*Of which date's interest rate should I use?

This is ungrammatical. To begin the question with the preposition, you could say "Of which date should I use the interest rate?" This is, however, hopelessly stuffy sounding. Even if you want to sound stuffy, this is difficult to understand and should be avoided.

Which date's interest rate should I use?

This is a reasonable choice.

What date's interest rate should I use?

This isn't as good, but it wouldn't be surprising to hear a native speaker utter this question.

In some contexts, it might make sense to make the question longer. For example, you might ask Which date should I use for the interest rate? In other contexts, you might be able to make the question shorter, as in Which date should I use?