The correct answers are Are there any tomatoes left in the fridge? and There aren't any clean plates for the dessert.

When asking questions or making negative statements, the same rules apply:

Use is there / there isn't for singular and uncountable nouns (e.g., a chef).

Use are there / there aren't for plural nouns (e.g., tomatoes, plates, potatoes).

"Is there any potatoes" is wrong because potatoes is plural. "There aren't a chef" is wrong because a chef is a singular noun.