1. He will give a golden apple to the man.

2. He will give a gold apple to the man.
[Can we use both 'golden' and 'gold' in the sentence?]

3. She has a golden watch and a golden bracelet.
4. She has a gold watch and a gold bracelet.
[In the sentences, which one is right?]

A gold apple would be an apple-shaped ornament made of gold. A golden apple could be a piece of fruit covered in gold paint or something, so they would not be taken as the same. There is an apple variety called "golden delicious", which is a greenish yellow in color. Similarly, a golden bracelet might be gold-plated so that it looks like gold but is not solid gold. A gold watch or other jewelry would be one that is solid gold or gold alloy. So, they are not really interchangeable.