What would happen if the mantle convections and the plate movement stop?
If mantle convections and plate movement stops, this means that the core has cooled down to a point where convection currents cease. If the core has cooled to that degree then the Earth will lose its magnetic field and all our traditional megnetic compasses will not work. This will cause problems with our transportation systems, although I think we can probably work around that one. No magnetic field may cause issues with how charged particles coming from the sun continue to be deflected to the poles. This may cause problems with health or our electrical systems. Earthquakes and volcanoes would cease. Any processes reliant upon geothermal energy would stop working.