The ball-valve is scaled up inside the cistern, and sometimes sticks. What is the best method to clean and inspect it?

Try some thick lime-scale remover, like LIMELITE. Pour plenty on, leave for about 10 to 15 minutes, to let some chemical action take place on the surface scale. Then use an old toothbrush to mechanically remove any loose scale bits, taking care not to damage the float-arm and float (some TORBECK VALVES have fairly thin float adjuster rods). Repeat the application of lime scale remover, and brush again if necessary. Pour some warm water over the valve to ensure that the lime scale remover is swilled off, and flush a couple of times, ensuring that the float arm moves down when the water level drops as the cistern empties, and will shut the water off when the float-arm is roughly horizontal. A good water level is about 2 inches (4 to 5 CM) below the top of the overflow pipe. If the valve still sticks, it may need replacing.  more