Is it possible to add the coloring range as legend?

You can extract the Point primitives and their styles from ListPointPlot3D output and use them to construct a PointLegend:

lpp = ListPointPlot3D[pointsChar, 
   ColorFunction -> Function[{x, y, z}, Hue[Sqrt[x^2 + y^2 + z^2]]], 
   Filling -> Axis, BoxRatios -> {1, 1, 1}, 
   PlotStyle -> PointSize[Large]];
legend = PointLegend[## & @@ Transpose[Cases[lpp, {a_, Point[b_]} :> {a, b}, ∞]], 
  LegendMarkerSize -> 20];

Legended[lpp, legend]

ClearAll["Global`*"]
pointsChar = {{0.`, 0.`, 41.63`}, {8.50479382206883`, 0.`, 
    31.74032265185878`}, {14.975`, 0.`, 
    25.937460843343935`}, {19.69999492385721`, 0.`, 
    19.69999492385721`}, {23.053596248741755`, 0.`, 
    13.31`}, {25.12373074177866`, 0.`, 6.731883363116563`}, {26.16`, 0.`, 
    0.`}, {26.205567667222418`, 
    0.`, -7.0217606936313866`}, {24.595121467478055`, 
    0.`, -14.2`}, {21.630396436496486`, 0.`, -21.630396436496486`}, {16.62`, 
    0.`, -28.786684421794742`}, {10.396761041768258`, 
    0.`, -38.80124044203187`}};

{minDist, maxDist} = MinMax[EuclideanDistance[{0, 0, 0}, #] & /@ pointsChar];

Since colors given by Hue are the same for min and max values, an alternative color function may be desired. Further, the EuclideanDistance is given in the Tooltip.

Manipulate[
 Legended[
  ListPointPlot3D[
   Tooltip[#, EuclideanDistance[{0, 0, 0}, #]] & /@
    pointsChar,
   ColorFunction -> 
    Function[{x, y, z}, 
     If[cf === Hue, Hue, ColorData[cf]][
      Rescale[Sqrt[x^2 + y^2 + z^2], {minDist, maxDist}]]],
   ColorFunctionScaling -> False,
   Filling -> Axis,
   BoxRatios -> {1, 1, 1},
   PlotStyle -> PointSize[Large]],
  BarLegend[{If[cf === Hue, Hue, 
     ColorData[cf][Rescale[#, {minDist, maxDist}]] &], {minDist, maxDist}}]],
 {{cf, Hue, "ColorFunction"}, {Hue, "Rainbow", "TemperatureMap"}}]