1) Depending on the temperature and what type of nucleus, one could infer the orientation of said nucleus. In addition, one could infer the energy transition frequency required for populating the hyperfine levels.
2) At low temperature, very weak thermal fluctuations can take place. As such very low additional energy will be present and thus most particles will try to populate the lower energy states. Whether or not the higher levels will be populated depends on how low the temperature is and how much of the lower levels is populated.