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So according to 1 and 2. There is no such thing as a submitting muslim who is not a momineen ?
So by definition ALL people who say shahadah are momineen ?

You need a Number 3 !

Well, you are right in terms of LAW only.

By LAW,
Anyone who says Shahada is Muslim as well as Momin. So if you have two sons, one is very pious and other is very evil, both are still 100% Momineen both will inherit your property with equal share. Your pious son cannot inherit your property more than your evil son. This means, Iman does not increase or decrease in terms of LAW.

By FAITH
Iman does increase and decrease, no one knows anyone’s Iman except Allah (swt) knows that person is Momin and how much Momin.
Iman is a state of heart, when you do good deeds, your Iman increases and you get closer to Allah (swt), when you do bad deeds, your iman decreases and you get farther from Allah (swt).