Typically, you build your character mesh so it only has the body. Then, you set up the rig/skeleton so that it has (appropriately placed) nodes for the hair, armor etc.
Then at run time, you hook up a left/right button to a list of your available meshes (for, say, hair) and make it so when the user clicks the button, it attaches the mesh to the proper bone.
As for switching the textures, you’d want a similar setup, but just to change the material instead.