I'll try to cover everything you asked here, and a few things that may be confusing you...

The tutorial having separate pieces for the mesh:

This is typically done for low rez representations of a character (though the tutorial mesh doesn't look low rez). It allows you to parent constrain the different pieces of the mesh to the joints so that you can get a "feel" for how the mesh will move once it is skinned. this is often used by the animator, as it gives a good visualization of the characters movements without the heavy calculations involved in working a skinned mesh (which can really bog down a computer).

Showing just the skeleton:

There are two methods of doing this that are both very easy. The first (and easiest for quick views) is, in the viewport menus, select Show > none, then Show > Joints. this will display only joints in that viewport. You can then go Show > All to see everything again. This is a very useful tool when rigging (IMHO), I often Have my viewports set up in 3 panels, one large hypergraph in the bottom, and 2 perspective windows side by side in the top, with one showing just the skeleton and rig controllers and the other showing the mesh without joints.

The other method is to use your layers. place all your polygons (edit >select by type > polygons, or hand pick them in the viewport, hypergraph or outliner) and place then on a new layer, you can then adjust the visability of the layers content (I'm going to have to direct you to the docs for learning more on layers and how to use them.

Your Skeleton:

It was just the angle your previous pics were on that confused me (It looked like one of your arms joint chains was a second spine. I was mistaken), The skeleton looks fine (could use a few more spine joints though).

How to get the mesh to move:

Smooth bind skinning will actually deform the mesh based on the joints that are influencing it. An easy example to demonstrate. open up the script editor Windows > General > Script Editor. In the bottom half, copy paste the bellow script into the box, highlight the entire script and select Command > Execute. you can rotate the joint thats already selected and see how the mesh bends with the skeleton.

polyCylinder -r 1 -h 5 -sx 20 -sy 5 -sz 1 -ax 0 1 0 -rcp 0 -cuv 3 -ch 1;
joint -p 0.0549451 -2.472527 0 ;
joint -p 0 0 0 ;
joint -e -zso -oj xyz -sao yup joint1;
joint -p 0 3 0 ;
joint -e -zso -oj xyz -sao yup joint2;
select -r joint1 ;
select -tgl pCylinder1 ;
SmoothBindSkin;
select -r joint2 ;
setToolTo $gRotate;

Skinning is done by selecting the root joint, the mesh and (in the animation menu set) Skin > Bind skin > Smooth Bind [Option Box] and set to default till your more confortable with skinning. At this point, I will need to direct you to tutorials and the docs for more information on skinning and weight painting.