I'll try to answer some that I know of....

General Questions:
1) How many watts does the stock lighting coils produce at 3K, 5K, 6K?
2) How many volts does the stock lighting coils put out at idle?
3) How many watts does the stock tail light with standard incandescent bulb pull?

• Stock lighting coils output 80watts max.  I only seem to remember this is above 4k RPM or so.
• I've only measured the stock lighting circuit (regulated) and it varied between 13volts to 17volts around idle.
  
• Stock tail light is an 1156 bulb base that is rated for 5 watts.

LED Light & Load Specific Questions:
Headlight:
Questions:
1) Will this stop the strobing?
2) Will a full signal bridge rectifier increase the volts to the light?  If so by what percentage?

• Good question.  It might.  I believe that the strobe effect is due to the Alternating Current IMO.
• Out of my scope of knowledge.

Lighted Whip:
Questions:
1) If I put a full signal bridge rectifier before the lighted whip, will it increase the DC amps above the 12v A/C signal coming from the stock voltage regulator?

• Sorry don't know this either. I just removed the stock regulator and added a regulator/rectifier for my battery and lights.

Entire System:
1) If I'm running this headlight at 36Watts, the Lighted Whip at 25 watts, and a stock tail light I'll be at approximately 71 Watts.  Since I am reaching what I believe is the watt limits of the system (55-60W, I could be wrong) will this increase the amps as there is not enough watts to push the electrical signal, to a point I'll over heat or burn up the system/ coils?

IMO, trying to run this much of a load without a battery will tax the stator/lighting coils.  My 12volt battery provides an electrical buffer to the stator.

My friend has picked up the new Baja Designs 9k lumens Squadron XL Pro light.  This draws 80 watts.  He has a Ballistic battery and initial testing shows it works.  Long term... I don't know. 

I've melted a set of the 130 watt lighting coils mounted to a stock stator.  Looking back now, it could of been caused by my poor ground on my initial build in 2010.  I was running a 4k HID light at the time.

Good luck with your endeavor