Stove top/cook top parts help?

[ha98ed14]

We have a gas cooktop set into the counter. It has (what looks to me like) enamel-over-metal pans/trays that sit depressed and surround the burners (where the gas comes out). On top of that, over the burner, sits a cast iron (? I think) grate, on which you place the pot or pan that you will cook with. Can anyone tell me what these pieces are called AND can I put them in the dishwasher? Where would you buy replacements? FWIW, the pans and grates are rectangular and cover two burners each. It's a 4 burner stove, so there is one pan & grate covering right burners and one set on the left burners.