Hi, both he 禾 and mai 麦 seem to mean Wheat. When do the Chinese use one and when do they use the other?

禾 is the general term for all cereals and grains. It includes rice, wheat, maize, barley, etc...

麦 can be either 小麦 wheat, 大麦 barley or 燕麦 oats.

Oh, I have a similar question as well.
What is the difference between 恶梦 and 噩梦, if there is any?

According to zdic.net
恶梦 - 使人恐惧的梦,或广义地指引起难以摆脱的恐怖的幻象或经历
恶梦 - 同“噩梦”
噩梦 - 引起极度不安或惊恐不已的梦
So they are the same. The only difference is that there is an adjective 极度 in the definition of 噩梦. So, may be 噩梦 is more severe.

According to the dictionary provided by the Taiwan MOE at http://dict.revised2.moe.edu.tw/index.html
惡夢 - 可怕或不吉祥的夢。
噩夢 - 惡夢，不祥的夢。
These also indicate that they mean the same thing.

Being kicked out of the Olympics is an 噩梦:

http://2012.sina.com.cn/cn/bd/2012-08-01/210532491.shtml