It's called D-Sub or VGA cable.
CRT monitors use a beam of electrons to form the picture - LCD's use microscopic pixels. CRT's need large amounts of electricity to form the picture - LCD's work with low voltages.
CRT: Use more power, lower resolution LCD flat screen: price
Yes, you would use only one of the video connectors at a time. The reason some monitors have different video connectors is to allow it to connect to a number of different video cards. If you have a DVI or HDMI connector on both the motherboard or video card and the monitor, then use it, and if not, use the VGA connector. Just use the one that is on both the computer and the monitor, and if you have both, just use the one you prefer.
CRT monitors are generally only still useful in harsh environments where an LCD monitor would not last, such as due to vibration, heat, or dust / debris.
flat-panel
No, unless you are still using a CRT monitor.
The decorder needs to have a VIDEO output, some do and some don't. Connect the video output to the tv's video input. These connections might be the R G B connectors or a HDMI connectors, these will be the best to use.
If your question is "does the use of a 17" CRT effect the power consumption of a dual core processor", the answer is no. The total power consumption of your system can depend on the monitor you use but, the power consumption of the processor is fixed by design not the monitor used.
connectors are use to connect into the port
You can get products that can turn any monitor into a TV with various inputs.
At this point, I would say that a CRT had no advantages over a LCD monitor. The LCD is probably cheaper, it takes up less space, is easier on the eyes, and provides better revolutions.
CRT (cathode-ray tube)