Lon, I will answer these, but you must promise to answer my last post.
I think you simply misunderstand O.T.. You make will make a pretty lousy calvinist.
1) How is foreknowledge of God different than predictability?
There is no black and white answer. Sometimes God predicts, sometimes he plans, sometimes knows, sometimes he sees. Let me start with a comparison. The S.V. usually think God is outside of time, and that is how he can see the future. Or they think he created the future, so he knows everything because he made it happen (ordained it).
The Open view says that God does ordain some things, but not everything. Whatever he ordains he foreknows. The open view shows verses that place God in time.
God can also predict, and when the decisions of the freewill agents are already made, he will know exactly what will happen. So prediction becomes knowledge. Remember, God has perfect present knowledge. So a prediction for him isn't like a prediction for us.
God can also plan. But he allows his plans to change because of his mercy for us. If he plans to destroy Nineveh, and they repent, he can change that plan. Not however, if God had perfect future knowledge and knew he wasn't truly going to destroy Nineveh, he could never say he would do it and at the same time not lie (even if he lied to bring about good, it is still a lie).
2) How is foreknowledge possible if, as the OV says, the future hasn't happened yet? Does this answer negate the definition of foreknowledge?
I answered this above. But in brief, he ordains some things to happen. Even though free will agents are involved, he ordains things. God uses our obedience or our disobedience to his advantage to bring things about.
3) Is there a way to determine in OV theology when God knows and does not know future?
Yes. Take Job for example. God did not know if his dedication was because of his blessings, or because of his righteousness. So he allowed Satan (who accused Job in the first place and was willing to test him) to test him.
Anytime there is an aspect of a persons life that a decision on how to act has not been made, God doesn't know it either.
4) How does God's knowledge of what we will do and what we are doing differ?
Huh?
5) What does knowing our intimate thoughts, motives, and desires mean to God? How is it different than how we think about this? (I'm trying to show a gap here. God is different than we are and knows what we do not nor cannot).
God knows everything in the present and past. He even knows our tendencies that are presently defined. He does not know things about us that are not defined by us yet. EG, he knows how many hairs are on our head.
6) Do we share in this attribute at all? Do we have any real kind of foreknowledge?
Sometimes we do. But our plans are second to Gods ultimate will.