How can my shrinkwrapped clothes stay on top of my character's skin when I animate? I have been using Blender for 2 weeks now. I have never done 3d animation before but I have been doing 2d animation since 2004. I manage to grasp a lot of the stuff in Blender (or 3d in general) like modifiers, meshes, IK and stuff. My problem is I have created clothes for my character, when I animate the guy his clothes start tearing apart in random places. 

The shorts where made by selecting regions of his legs and then I duplicated them into a new mesh (shift D or control D or something). The "shirt" was made using bsurfacing starting from a single vert. 

Neither object has cloth modifies (cause I'm not sure how to do that and not get problems) and there is no gravity on the garments (I don't think I want it) and neither garment has a collision on them. 

Is there a way to make sure that my shrinkwrap modifier continues to hover on top of the guy's body/ flesh mesh without exposing his skin?

In the picture I have also show that the guy has a beard, I made that using a separate mesh. The beard is not attached to his chin, how do I do that? It got left behind when I moved his head.

The circled places in the attached image also show the shrinkwrapped clothes being torn apart by the guy's body when I animate.

Please help me!
I think you have problems with Weights. 
You can try transfer weights from character body to clothes: https://www.youtube.com/watch?v=stem2OPRAyA
About beard:
In object mode select beard, then armature. Press Ctrl + P and choose "Armature deform - With empty groups".
Then choose a beard, open edit mode. Select the beard and open data tab (on the left side of screen. It has the same label at your version of program. Find Vertex Group which is responsible for the head, choose Weight = 1 and click Assign.