The water is circulating by gravity which is the way it must be done with solid fuel.
Noises in the back boiler mean the water is starting to boil, it also may start pitching from the expansion pipe into the header tank in the attic.
You can usually relieve that by running the hot water tap. It sounds worse than it is, but it's not ideal.
You don't mention any downstairs radiators, which would probably be the purpose of the pump. The pump may be kaput or just stuck, there's usually a removable cap in the centre of the housing which gives you access to the shaft so you can free it up with a screwdriver.