You can change the colors with PlotStyle:
ListPointPlot3D[{Table[x, {x, 20}, {y, 20}],
Table[y, {x, 15}, {y, 20}]}, PlotStyle -> {Pink, Green}]
The points are not spherical enough? You can try with something like
With[{r = .1},
Graphics3D[{Red, Map[Sphere[#, r] &, data1], Green,
Map[Sphere[#, r] &, data2], Blue, Map[Sphere[#, r] &, data3]}]]
adapting the radius r to your needs.