Should I have crowns to all my back teeth which are heavily filled and some discoloured?
I only have pain in one of them. There are 10 crowns proposed. What are the advantages or disadvantages?

Crowns add strength to your teeth. Heavily filled teeth are at a higher risk of breaking. Sometimes when they break the only thing that can be done is remove it.
You may not notice any advantage right away but as time goes on you will have fewer fillings falling apart.
The one that is causing pain should be addressed first.