As you can see on the attached picture I get all the time these sticky meshes when I am parenting the bones to the mesh, I have even made an obj file with another
rig and parented these together, but none of these did help. Do I have to reset
Those pointy bits are individual Verts that are not assigned to any Bone. With the Armature in Pose mode, RMB-select your Mesh and Ctrl-Tab into WeightPaint mode, RMB-select the bone(s) in the fingers and the head, one at a time and paint those pointy bits red so they get sucked to where they belong.
I understand the trick, I think, I will try it out.