I think you've understood it. Its is always possessive. It's is always short for either it is or it has.
1. She enjoyed the movie and told me it is scenery reminded her of her hometown. Not make sense. You are right 'it is/it's does not make sense here. So it is possession and should be its. The movie's scenery = its scenery.
2.You really ought to take up fly-fishing---it is a very relaxing hobby. It makes sense. Correct, so you'd use 'it's' here.
3.This is a fine piece of furniture, and it is merits speak for themselves. Not make sense . You are right so see sentence one comment.
4.She wants to study music in all of it is various genres. Neither this sentense make sense.. You are right so see sentence one comment.