1. What exactly is Cura, and is it necessary if you have software that generates .stl files? I have and am proficient in Sketchup and Rhino3d. Both export to stl.
Cura is a slicer/toolpath generator. Cura takes your STL file and converts it to G-Code (something the printer controller can understand and convert to motion, etc.)

2. Based on it's properties, I'm hoping to print ABS. It seems bed temperature control is critical for ABS and many people recommend enclosing the unit and/or insulating under the heat bed. (I watched a few of the videos on this.) I wondered if anyone tried using computer thermal paste between the heat bed and the glass plate? It occurred to me it might facilitate faster heat transfer and reduce heat up times. The reason you use thermal paste in PC applications is to make sure that there is no air gap between the CPU and cooler, as the air would heat up very quickly. That isn't an issue in a heating application.

3. I intend to build bicycle parts and chose ABS for the strength and better outdoor properties. It there another filament that might be better for my purposes that is compatible with the CR-10?
ABS degrades over time when exposed to UV light (ie. the Sun), if ABS has a suitable enough strength for your application, ASA material would alleviate the issue. If the parts are structural, consider more sophisticated materials like carbon filled or nylon. They won't print easily on a stock CR-10 though..