First of all, if you've transcribed the question correctly, there's a grammatical error in it. It should be:
In order to enhance the ........... of the salad plate, lay some shaped tomatoes in the center.
Now, with regards to your questions:
What's wrong with variety?
The clue is in the second half of the sentence. Variety refers to a range of things, and enhancing a variety would be adding more different types of things to that range. However, the verb used is lay, which refers to the positioning (and by extension, the look) of the salad plate. If lay were swapped with a word like add, variety would be the correct choice.
Does the sentence above make sense to mean 'I was amazed by different ingredients used in the salad'? If not how should I edit the sentence? Is there a different word to do that?
As is, I would parse the sentence as you being amazed at the different types of salad available, not the ingredients within the salad. There are a few ways to go about changing the sentence. You can be more explicit and mention the ingredients directly:
The variety of ingredients in the salad amazed me.
You can also be more general by referring to the variety in the salad.
The variety within the salad amazed me.