1) As the nucleus has a spin of 1, it can be oriented in three ways, namely m_I=0 or plusminus 1. Of these orientations a spin in the +1 direction, so along the magnetic field axis, will have the lowest energy. The size of the hyperfine energy splitting will give you the size of the Bhf. From the distribution of the states occupied in the energy levels, the oriëntation distribution of the nuclei in you ensemble can be directly deduced.
2) At low temperature, so below 1 mK if the energy difference between the levels is about 1 µeV, the lowest energy level (so with an oriëntation along the magnetic field) will be occupied the most, as dictated by the Boltzmann distribution: N=N_0exp(-E_i/kT). The amount of states occupied in the subsequent levels will be exponentially lower. If the temperature is close enough to absolute zero, virtually only the lowest energy level will be occupied.