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I experience a texture error whenever I try to render my Project.

CINEMA 4D has 5 locations that it references when searching for texture images. 
1. The same folder as the Project file
2. A Tex folder in the same folder as the Project file
3. The CINEMA 4D application folder
4. A Tex folder in the CINEMA 4D application folder
5. The alternate texture paths set in the Preferences menu
   
When you load the image into a material, CINEMA 4D will prompt you with a message. It asks you whether or not you want to create a copy of the image to the document's location. Choose Yes. This will place the graphic in a search path that CINEMA 4D recognizes. A good practice for organizing projects is to use the Save Project command when beginning the Project to set up a folder to which the textures will be copied.

Alternatively you can create texture paths in the Texture tab of the Preferences menu. Click on the File tab to view the texture path settings.

How do I apply separate materials to the caps and roundings of NURBS objects?

NURBS objects have invisible selection sets for their caps and roundings. Materials can be applied to these specific areas by using the Restrict to Selection field in the texture projection window. 

Below are the names of the hidden selection sets:
C1 = Cap 1 (front)
C2 = Cap 2 (back)
R1 = Rounding 1 (front bevel)
R2 = Rounding 2 (back bevel)

Be sure to use capital letters C and R.

Why doesn't the pixel length of my texture match the pixel length of my object in CINEMA 4D units?

There is no relation between image size and geometry size. It is impossible to have a relation between these two. Instead, the pixels are only relevant to render size. Hence, you can set the render size to the same pixel length as your texture and position your camera so the cube face fills up the entire screen.

However, it would probably be much easier to just fit the texture to the selection.

What does the Additive check box in the Transparency channel do?

By default, increasing the transparancy of a material reduces the color strength, producing a natural-looking effect. Checking the Additive box will disable the default behavior and will not reduce the color strength. Use this option with care as it can create unnatural-looking materials.