As a toy, Jar has no blood, instead he has a huge amount of synthetic fiber inside. He does't feel pain, but every time he is injured he may feel a little discomfort (so that he at least knows that he is injured). Huge wounds, such as canonical ones, can only be sewn together
About the fire on he's hat: Do y'all remember that bug with fire in minecraft? When you die from fire, you can continue to burn for a while after respawning. The fire on hat cannot be extinguished, but also the fire can't damage Jar or the surrounding area.