There are many things that God has done/is doing/will do that I cannot explain Yeshua and to which portion of the scripture are you referring concerning the Messiah coming and giving us a new heart?
As for the second question that is somewhat knowable: IMO there is a difference (which I have said all along) with the relationship between the OT and NT believer (though both were regenerated) and the Spirit because of the use of future tense verbs in the NT.
Matthew 3:11 I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire:
He comes after John and at that time He was not yet baptizing us in the Holy Ghost (indicative, future, active - not yet a reality)
Matthew 16:18 And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.
Active indicative future tense - NOT YET a reality, there is no way to slice/dice this to make it say anything else. There are special ministries related to the church as an institution which has an effect upon individuals.
Regeneration is regeneration, but OT regeneration does not have to relate 100% and its subsequent affects with NT regeneration and its following events. So what? God does as He pleases without checking our systematic theologies before He does anything. e.g. Regenerate OT men wrote inspired scripture:
1 Peter 1:11 Searching what, or what manner of time the Spirit of Christ which was in them did signify, when it testified beforehand the sufferings of Christ, and the glory that should follow.
Biblicist has shown others.
Yeshua, read 1 Corinthians and then the first 3 chapters of Revelation: then ask yourself this question:
Have we (NT saints) done any better in really obeying Him than the OT saints though we are regenerated, indwelt and sealed with the Spirit?
HankD
Yes, as they did not have him within them the Holy Spirit in same measure/fashion that we do have Him now under the new Covenant.