Plot a contour of concentration profile for a sphere

Question

Assuming a linear concentration profile in a particle(sphere), I managed to make a SliceContourPlot3D for 2 linear concentration functions(a function of radius). I met some problems here:

1. There are some strange curve appeared on the surface of the sphere. Others are on the back side.

Fig.1

2. Is it possible to unify the barlegend or gradient color? The maximum concentration for Fig.2 is 10, corresponding to color level below 10 in Fig.1. Is there a way to color it as shows in Fid.1?

Fig.2

3. I tried to make the ContourPlot for this sphere, but failed.

    R=0.001;
    expr1=TransformedField["Spherical"->"Cartesian", 50/0.001 r,{r,\[Theta],\[CurlyPhi] }->{x,y,z}]
    SliceContourPlot3D[expr1,{"CenterCutSphere"},{x,-R,R},{y,-R,R},{z,-R,R},ColorFunction->ColorData["BlueGreenYellow"],PlotLegends->BarLegend[Automatic,LegendMarkerSize->{10,200}]]
    ContourPlot[expr1,{x,-R,R},{y,-R,R},ColorFunction->ColorData["DarkRainbow"],PlotLegends->BarLegend[Automatic,LegendMarkerSize->{10,200}]]
    
    expr2=TransformedField["Spherical"->"Cartesian", 10/0.001 r,{r,\[Theta],\[CurlyPhi] }->{x,y,z}]
    SliceContourPlot3D[expr2,{"CenterCutSphere"},{x,-R,R},{y,-R,R},{z,-R,R},ColorFunction->ColorData["BlueGreenYellow"],PlotLegends->BarLegend[Automatic,LegendMarkerSize->{10,200}]]