Hello, Hela.
Your analysis of the first sentence (I gave my sister a cat for her birthday) is correct. I'd be happy with calling the prepositional phrase "for her birthday" an adjunct (adverbial) of time, though some more accurate label may exist.
It's true that R. Quirk does not consider the sentence pattern SVOdOi. He'd call "to my sister" in your sentence #2 an adverbial. I am no grammarian, but I disagree. If "my sister" is the I.O. in the first sentence, why can't it still be I.O. in the second? There has been only a change of position of that noun phrase, but that does not involve a change in the meaning of the sentence. The indirect object needs to be introduced by a preposition (usually "to" or "for") when it is places after the D.O. To me, "to my sister" in sentence #2 is exactly the same I.O. as "my sister" in sentence #1.
The verb "give" in your second sentence is not complex transitive. Complex transitive verbs take both a direct object and an object complement, which is not the case here. If we follow Quirk and say that "my sister" is an adjunt (adverbial), then "give" is a monotransitive verb. If we say that "my sister" is the I.O. of give, then the verb is ditransitive: it takes two objects.
Your example #3 could be analysed in the same way, I think. "Of" is not the usual preposition that will introduce an I.O., so you can say that "of the Supreme Court Justice is an adjunct (adverbial). However, that structure might also be considered the I.O. of the sentence. You have two possible passive counterparts for your sentence: "The Supreme Court Justice was asked a question" and "A question was asked of the Supreme Court Justice!.
That said now, I think you can make your choice (I.O. or adverbial) and either should be ok, since both can be accounted for.
As a side note here, I'll mention that Quirk also poses a dilemma when it comes to analysing certain verbs such as "look at". He says that, in a sentence like "I'm looking at you", you can consider the preposition part of the verb, in which case "you" would be D.O. But, he says, you can also consider "at you" as a prepositional phrase, in which case it would be an adjunct (adverbial) modifying the verb "look".
Miriam
P.S. If "of the Supreme Court Justice" were an adverbial, as you say, I'm not sure what type it would be, but you can have adverbials of almost anything (yes, this is a bit of an overgeneralisation!). Perhaps one of target or goal if such things actually exist?