My friend, if you want to say something is upon the another things, you can use this pattern: .......something+上（Shàng） for example: 书在桌子上。Shū zài zhuōzi shàng.The book is on the table. 花儿在电视上。Huār zài diànshì shàng.The flowers are placed on television. I hope my explanation help you. Good luck!~

1，我把你绿色盘子里不含麸质的食物放你桌子上了。 you need to divide ON... ON... into several groups. Like the GREEN PLATE is a phrase discribe GLUTEN-FREE FOOD, so you need to put it in the front of food because adj. words/phrases should be in front of the n. 2，钻石在桌子上的盘子里。 in this sentence "on a saucer on the table" is a group which describe where the diamonds are, so if you follow the rule you should say "钻石在盘子里、桌子上“ However, in fact there is no such sentence in Chinese. So instead of saying "钻石在盘子里、桌子上“, you need to translate ON A SAUCER as an adj. phrase.

我把你（要）的不含谷蛋白的吃的放在书桌上的绿色盘子里了。 钻石在桌上的（一个）碟子里。