You have misunderstood the no-cloning theorem. The theorem sez the following. Suppose you have a quantum system S in an arbitrary state $|\psi\rangle_S$. There is no physical process that can take that system and copy its state to another system in a blank state $|0\rangle_C$. That is, no physical system can perform the operation $|\psi\rangle_S|0\rangle_C \to |\psi\rangle_S|\psi\rangle_C$ for an arbitrary state.

The no-cloning theorem is perfectly consistent with being able to prepare two different systems in the same state to an arbitrarily good approximation since this doesn't involve copying. In addition, if you have many systems prepared in the same way you can perform measurements to find the state in which the system was prepared to any desired degree of accuracy - this is called quantum tomography:

https://arxiv.org/abs/1508.01907

You are also confused about what the amplitudes mean in quantum mechanics. The square amplitude $|\psi|^2$ only acts as a probability when the system concerned has undergone decoherence. Before the system has undergone decoherence, the square amplitude can change in ways that break the rules of probability:

https://arxiv.org/abs/math/9911150

https://arxiv.org/abs/quant-ph/0306072

You have misunderstood the no-cloning theorem. The theorem says the following. Suppose you have a quantum system S in an arbitrary state $|\psi\rangle_S$. There is no physical process that can take that system and copy its state to another system in a blank state $|0\rangle_C$. That is, no physical system can perform the operation $|\psi\rangle_S|0\rangle_C \to |\psi\rangle_S|\psi\rangle_C$ for an arbitrary state.

The no-cloning theorem is perfectly consistent with being able to prepare two different systems in the same state to an arbitrarily good approximation since this doesn't involve copying. In addition, if you have many systems prepared in the same way you can perform measurements to find the state in which the system was prepared to any desired degree of accuracy - this is called quantum tomography:

https://arxiv.org/abs/1508.01907

You are also confused about what the amplitudes mean in quantum mechanics. The square amplitude $|\psi|^2$ only acts as a probability when the system concerned has undergone decoherence. Before the system has undergone decoherence, the square amplitude can change in ways that break the rules of probability:

https://arxiv.org/abs/math/9911150

https://arxiv.org/abs/quant-ph/0306072