Is The word foreknowledge In Acts 2:23 in the instrumental dative case? Does foreknowledge mean omniscience, or is it an attribute of God?
Here's the answer to your first question, according to A.T. Robertson (Word Pictures in the New Testament):
Act 2:23 - Him (tou'ton). "This one," resumptive and emphatic object of "did crucify and slay." Being delivered up (e[kdoton). Verbal adjective from ekdidwmi, to give out or over. Old word, but here only in the N.T. Delivered up by Judas, Peter means. By the determinate counsel and foreknowledge of God (th'/ wJrismevnh/ boulh'/ kaiV progwvsei tou' qeou'). Instrumental case. Note both purpose (boulh') and foreknowledge (progwvsei) of God and "determined" (wJrismevnh/, perfect passive participle, state of completion). God had willed the death of Jesus (Joh 3:16) and the death of Judas (Ac 1:16), but that fact did not absolve Judas from his responsibility and guilt (Lu 22:22). He acted as a free moral agent. By the hand (diaV ceiroV"). Luke is fond of these figures (hand, face, etc.) very much like the Hebrew though the vernacular of all languages uses them. Lawless men (ajnovmwn). Men without law, who recognize no law for their conduct, like men in high and low stations today who defy the laws of God and man. Old word, very common in the LXX. Ye did crucify (prosphvxantej). First aorist active participle of prosphgnumi, rare compound word in Dio Cassius and here only in the N.T. One must supply tw'/ staurw'/ and so it means "fastened to the cross," a graphic picture like Paul's "nailed to the cross" (proshlwvsa" tw'/ staurw'/) in Col 2:14. Did slay (ajneivlate). Second aorist active indicative with first aorist vowel a instead of o as is common in the Koine. This verb anairew, to take up, is often used for kill as in Ac 12:2. Note Peter's boldness now under the power of the Holy Spirit. He charges the people to their faces with the death of Christ.
For your second question: I would say that foreknowledge and omniscience are attributes of God, although in Acts 2:23 the emphasis is on the fact that while sinful men rejected and crucified the Lord of Glory, it was all in the predetermined plan of God. To paraphrase Peter's words he is saying something like this: "Jesus was the Son of God, and He proved it by many signs and miracles, but in spite of this wicked and sinful men nailed Him to the cross. This was no accident, for long ago God purposed that this would happen. Sinful men did not know it but even in their wickedness they fulfilled the purpose of God for His Son to die on the cross of Calvary, bearing the sins of men."
The thing you have to watch out for here is that "foreknowledge" in this text does not mean "to know about ahead of time" though God certainly does know. Foreknowledge here means to determine ahead of time. The verb for "foreknow" is used with the sense of "know about beforehand," as it is in 2 Peter 3:17. But it is also used with the sense of "to determine or choose or appoint beforehand," as you can see in Romans 11:2 and 1 Peter 1:20. God did not merely "know about Israel ahead of time," God chose Israel (Romans 11:2); and God did not merely know about the coming of Christ, He predetermined it (1 Peter 1:20).
On the attributes of God, you may want to look at the series I did on this subject which is on the Biblical Studies Foundation Website.
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