Is God omnipresent and omniscient? Here are some common cites used to claim otherwise:
Gen. 11:5 But the LORD came down to see the city and the tower that the men were building.
Ps. 14:2 The LORD looks down from heaven on the sons of men to see if there are any who understand, any who seek God.
In these verses, what we have is not an indication that God is not omnipresent/omniscient, but a choice bit of satire/irony at the expense of man. As Evangelical scholar John Wenham puts it: "The tower which men thought reached to heaven, God can hardly see!" [John Wenham, Genesis 1-15, 246]
Men thought their tower was spectacular; but the writer wants us to view it as so unspectacular, puny and irrelevant that an omnipresent God didn't notice it until He came closer. Likewise, the number who seek God is so small that even an omniscient God has to look for them.
Gen. 18:21 ...I will go down and see if what they have done is as bad as the outcry that has reached me. If not, I will know.
2 Chron. 32:31 But when envoys were sent by the rulers of Babylon to ask him about the miraculous sign that had occurred in the land, God left him to test him and to know everything that was in his heart.
This verse set is somewhat different. In Genesis, the word "outcry" is a technical legal term for a cry for help from a great injustice. In Ancient Near Eastern jurisprudence, the judge would have to be present in order to make a judgment; a visible, tangible presence would be necessary. God was therefore exercising the role of an ancient judge.
This is obvious in that God incarnated as a human for this occasion; if this were only a matter of needing to come down and see because He was not omnipresent, the incarnation body is superfluous.
Finally, the word for "know" in both passages can also mean to recognize or consider and does not, in this context, imply a previous lack of knowledge.
1 Kings 19:11-2 The LORD said, "Go out and stand on the mountain in the presence of the LORD, for the LORD is about to pass by." Then a great and powerful wind tore the mountains apart and shattered the rocks before the LORD, but the LORD was not in the wind. After the wind there was an earthquake, but the LORD was not in the earthquake. After the earthquake came a fire, but the LORD was not in the fire. And after the fire came a gentle whisper. (Cf. also Num. 23:15, Job 1:12, Jonah 1:3, Gen. 3:8)
This relates to our third cite set, which refer to the presence of the Lord, or speak of someone meeting the Lord in a place. When it is stated that the Lord is not "in" the fire, wind, etc. it is contextually in reference to God's presence, or glory, which has nothing to do with omnipresence or omniscience.
One may relate this to the point that, in order for a transcendant God to enter a temporal world, it is needful to establish a point of presence of limited power -- a crossover into our temporal realm, as we Star Trek fans may say -- lest our world be destroyed by the infinite power of God.
At the same time, the main passage is didactic in nature: Elijah is being shown that God's will is found not in circumstances, but in what He says to the prophet (the gentle whisper). Indeed, even if omnipresence were not one of God's characteristics, this verse would be of no relevance, since even the least powerful pagan deities could be thought to inhabit natural forces. The negative statement of influential presence says nothing either way about omniscience or "physical" presence.
Then there is this sort of verse:
Gen. 22:12 And he said, Lay not thine hand upon the lad, neither do thou any thing unto him: for now I know that thou fearest God, seeing thou hast not withheld thy son, thine only son from me.
(See also Deut. 8:2, 13:3)
In all of these cases the word used for "know" is yada, which has broad connotations meaning knowledge (when something was not known before) or familiarity, or observation. In this sense it would suggest that God could not logically act upon human responses until the response was made.
Finally we have verses like this:
Gen. 3:9 But the LORD God called to the man, "Where are you?"
Ezek. 20:3 "Son of man, speak to the elders of Israel and say to them, 'This is what the Sovereign LORD says: Have you come to inquire of me? As surely as I live, I will not let you inquire of me, declares the Sovereign LORD.'"
The former may be an example of the sort of limited presence we have referred to, but I think that both of these are actually examples of how a typical ANE sovereign addressed his subjects (or any person addressed any person): In the form of a question, even when the answer is known. (Cf. Gen. 31:26; 1 Sam. 15:14; 2 Kings 5:25;