I am getting vibration through my pipes after flushing, it is also very slow & I am finding cement pellets at the bottom of the pan
Could be that the float/valve is causing this. If you flush the toilet and hold down the float, then let go when the tank is full (you might have to pull up on the float to close the valve quickly), do the pipes vibrate? If not, replace the valve assembly. If there is still vibration I'm not sure what else could cause this (except if the tank value didn't close all the way) because there's no other active valve in the system at that time. For just $5, replace the valve assembly.
When the water flows thru the pipes, the pressure and turbulence can force the pipes to vibrate, specially if those pipes are not properly secured to the studs. Sometimes when the shut-off valve (the shut-off valve is Not part of the toilet) is partially closed, the vibration will take place too. The cement pellets may actually be calcium/ mineral stones that form inside pipes over time and when they are large enough, the water flow pushes them out, into your toilet tank in this case. In other cases, this little stones clog your shower heads and collect in the mesh filters that most faucets have, causing a reduced water flow.