Is blue board& plaster fire rated

You'll need to be more specific with the brand name and specific product.

Most products (in the U.S.) for construction like you are speaking about are marked clearly (on the product or in the lituature) with their fire rating.

Maybe, depending on classification. National Gypsum uses the blue board but they must be rated X or C

Kal-Kore Fire-Shield Plaster Base features a fire resistive Type X gypsum core to provide additional fire resistance ratings when used in tested systems.
Kal-Kore Fire-Shield C Plaster Base panels have a specially formulated Type X core to achieve superior performance when used in specific fire-rated assemblies where the weight and number of gypsum board layers are a concern.