You are more likely to get higher scores if your element matches rather than opposes the arena's element. I put a plant in fire and got bronze, plant in plant and got gold. I believe that is the only difference.
I looked it up before too because I had a similar question. I did not find much on this actually, so I tested it myself and that outcome was always mis-match = bronze or silver match = silver or gold. (I unfortunately decided to test this after all my dragons were level 7, not 10 yet but all were at least 7 so many came out silver either way).
The Emerald Dragon can be bred by selecting a Crystal Dragon to mate with a Lichen Dragon at the Breeding Cave/Epic Breeding Island.
This wouldn't be the first time they've made a dragon only breedable by a single pairing (the Sakura dragon used to be), so I'd stick with that combo until more pairings are confirmed.
Interestingly, Emerald Dragons can't be bred with eachother:
The Emerald Dragon cannot be bred with any other dragon, including breeding with another Emerald Dragon.
Best Answer
You buy the shrine under the 'Buildings' section in shops.
You have to go to shop and navigate to 'Buildings'.