Item 2 is not compatible with Aquinas so it would not work with his system: “2) Soul is immaterial and doesn’t have any part”. For example,
Summa Theologica Q79, A9:
Reply to Objection 1. We speak of parts, in whatever way a thing is divided. And so far as reason is divided according to its various acts, the higher and lower reason are called parts; but not because they are different powers.
newadvent.org/summa/1079.htm
And Q77 A1:
Reply to Objection 7. Rational and sensitive, as differences, are not taken from the powers of sense and reason, but from the sensitive and rational soul itself. But because substantial forms, which in themselves are unknown to us, are known by their accidents; nothing prevents us from sometimes substituting accidents for substantial differences.
and Summa Theologica, Q77, A8:
I answer that, As we have said already (5,6,7), all the powers of the soul belong to the soul alone as their principle. But some powers belong to the soul alone as their subject; as the intelligence and the will. These powers must remain in the soul, after the destruction of the body. But other powers are subjected in the composite; as all the powers of the sensitive and nutritive parts. Now accidents cannot remain after the destruction of the subject. Wherefore, the composite being destroyed, such powers do not remain actually; but they remain virtually in the soul, as in their principle or root.
So it is false that, as some say, these powers remain in the soul even after the corruption of the body. It is much more false that, as they say also, the acts of these powers remain in the separate soul; because these powers have no act apart from the corporeal organ.
newadvent.org/summa/1077.htm