Hi Skandelon, I do not know what God knows, and neither, dear friend, do you.
We know all that need to know though, its found in the Bible...
Yes God can know our thoughts and motives, He can "search" our hearts. But He can also choose not to know our thoughts and motives and test a person such as Abraham. He does as He pleases. To assert God cannot limit His knowledge is to limit God and deny scripture.
Again, the testing was NOT to have God learn something He did not already know, its to "test" Abraham in the sense to allow him to show by his action what was already in his heart/mind to expose it ... Be like Thru paul, God saw his heart, know his faith and he would do it if need be, per James, his actions showed his faith and belief...
Do you believe God "did not know" what Abraham would decide to do until he actually did it?
And as for you last point, scripture says He can put your forgiven sins out of His view, behind Him so to speak, that He will not bring them to mind. That they will not be "before Him." So again to deny God has the power to limit His knowledge is to limit God and deny scripture.
No, its just that there are NO scriptures showing God can do that, chosen to do that..
There ARE just things God CANNOT do, as would go against His nature.Attributes "forgetting/not knowing" falls here
Jesus DID have limitations to Himself while in human form upon the earth he chose to "limit" not use His divine attributes, but exist and live as a man fully dependent upon doing will of His father In power of Holy Spirit
UNLESS you refer your line of reasoning JUST to Jesus while he was on the earth, cannot apply any of that to God... And Jesus right now has back fullness of His glory, so exercising ALL divine attributes once again, so not of yourr reasoning applies to God right now!
Final point, God can know what existing people, or people who lived in the past, would do if a circumstance arose, so He can say those people in that town would have repented if they had seen My miracles. But this does not support the assertion God knows what people who have not yet been conceived will do, unless God has predetermined what He will bring about in their lives.