Cheryl Schatz

Yes, the Spirit of Christ is the same Spirit as the Spirit of God.

While we can say that there is mutual submission in the Trinity it is a bit of a moot point since there is one will.  For example the Holy Spirit does not submit his will to the Father since there is no reason to submit.  They both have the exact same will.  Submission can be in relationship but again how does all of that work when they all share the exact same will?  There cannot be one will submitting to another will.  The submission that was shown in their relationship became known to us when the Word of God became flesh.  It was when humanity was added to his identify as God that there could now be a will (a human will that was added) that would be willing to submit.