Strictly defined, 'golden' refers to something that looks like gold and may or may not actually be gold. 'Gold' usually refers to something that is actually gold. However, in actual usage, nobody much pays attention to the difference and it doesn't matter too much.

A golden ring can be a bit broader of a term. Golden could be either a color similar to the color of gold - "she had beautiful golden hair" - or it can describe something that is made of gold, such as the golden ring you mention. Saying a "gold ring" just clarifies that it is really a ring made out of gold, eliminating the possibility it is just a ring that is golden in color. Either one is acceptable to use though.

There is a slight difference. Golden is not specific while gold is specific. U can say,she was wearing a golden colored gown,shoes,bag....I.e,it was the same color wth gold but not gold but gold is direct. U can say d both in any case.

I've heard that just wool and wood change into woollen or wooden but why gold?Can I change it too?

There is no difference, I think.