To those who are familiar with nuclear physics, I have two questions of understanding:

1. Why does it happen that nuclei have a spin greater than 1 (e.g. I=8 at 90Nb)?
2. How can we infer the parity of a nucleus?

My ideas:

1): I have the nuclear shell model in mind. If the levels for protons and neutrons are filled one after the other. In the case of "even-even" nuclei, all levels are fully occupied, so the total spin adds up to 0.
If we now have an odd number of protons and neutrons, then according to this model one level would only be half full. If the spins are parallel, this adds up to I=1.
But how do I get I=8 (or other integer values)?

To 2):
My idea about "even-even" nuclei: The total spin is 0, so the spin wave function is antisymmetric. Since according to the Pauli principle the total wave function must be antisymmetric, it follows that the local wave function is symmetric, i.e. the parity is positive.

Is this argumentation correct?

What about "odd-odd"-nuclei or "even-odd"-nuclei? How can we conclude parity here?

I would be very grateful, if someone could help me. Sorry if my text is not understandable in some places, English is not my mother tongue.