'North' is a direction. We often use it as an adverb e.g. 'Drive north'. 'The north' is a geographical area e.g. 'It rains more in the north than in the south'. 'Left' and 'right' work the same way. 'Go left' but 'The road is on the left'.

Both are possible (article/no article) ('the') "In the north of Australia there are many crocodiles" 'the north' is a specific region (within Australia) (no 'the') 'Papua New Guinea is north of Australia" 'north' is a non-specific region (beyond Australia)

I think it would help to be more specific. Are you talking about directions or places? Can you give examples? I think that there may be lots of rules, and lots of exceptions here.