They look like they have hard plastic under it. Is it plastic?

This insole is composed of three materials: the felt/topcloth lining, the gel insole, and a hard plastic frame at the bottom of the insole. However, it is important to note that the "hard plastic" isn't stiff or bothersome, rather it functions as the frame that give the tri-balance the shape necessary for it to support the heel and bridge of a person's foot. This bottom plastic layer is still pliable and flexible.

Will they work in sandals?

Probably, I never tried that! They are very comfy.

are these inserts good for flat feet and over-pronation?

I have Flintstone flat Feet, female, size 8. These inserts are a gift to the flat foot. I found them instantly comforting upon first walk. When my job was Full-time, ave day walking 10-11 miles. They only cover a short portion of the foot bed of your shoe. This is intentional. It's Graduated, like a beach shore. I see people barking they're made for a kid. NO. They are made for adult foot. They aid as intended.