Radiation from the microwaves passes through material such as glass, ceramic and plastic. Any current dinnerware made from those materials should be safe to use in the microwave. Most dinnerware sold today lists on the bottom whether or not it is microwave safe.
Older dinnerware and dinnerware from foreign countries may contain lead. These are not safe to use in microwaves.
Test the safety of dinnerware in the microwave by placing a piece of it alongside a glass cup full of water. Do not have them touching. Microwave on high one minute, and if the utensil is warm or hot it is unsafe to use.
Leaving a metal piece of flatware on the dinner plate as it is microwaved will certainly hurt the microwave. The radiation will reflect back to the magnetron and damage the oven.