Taking your post in pieces and out of order...
Eidolon, thanks for the great info. This should be a sticky.
Absolutely. Hopefully a few others, such as MFE or toedrag will also chip in on this, just to make sure my info is correct.
For ref. I uploaded a dyno graph of the LS3 that I found on the web. This may not be the extact one for a stock GXP M6..
The graph is informative because torque remains relatively level, but power continues to build even after the torque peak. In short, there's no reason to cut a gear short until you get north of 6000 RPM's. But even then, as power begins to fall off after the peak, it falls off less than the reduction you'd get by shifting (because shifting drastically drops your RPM's). In short, if you're going for maximum acceleration, wind it up to redline.
But for example I am driving on a highway in mexico. Cruisin 60-65 in 6th gear. All of a sudden another car pulls up in the next lane and wants to play. He honks off .....
do i downshift to 5th (Tried not effective) ?
do i then go the 4th (Tried not effective) ?
Go directly to 4th (Tried effective some times but not really)?
Go directly to 3rd (too chicken **** to try....)
If you're cruising at straight highway speed, you likely want to get to 3rd.
To get RPM's in a given gear at a given speed, do the following:
Wheel RPM = (MPH x 5280 X 12)/(83.93 x 60)
(Simplifies to MPH X 12.582, by the way.)
Engine RPM = Wheel RPM x Final Gear Ratio
(Verified: I'm usually turning just a tick under 2000 RPM at 75 MPH in 6th. Run the numbers through the formula above and 75MPH in 6th = 1990 RPM's)
So at 65 MPH, your engine will be turning approximately the following RPM's:
1st: 9108
2nd: 6264
3rd: 4327
4th: 3026
5th: 2542
6th: 1725
First is obviously right out. But this list does let us answer your next question...
What gear should I be in to make most effective use if the power band of the engine ? then what speed it would be ok to downshift to that gear and be safe?
As noted above, you want to shift into the "power band". In this case, that means close to your engine's torque peak. That's where you'll get the most acceleration in any given gear. For us, that's right around 4600 RPM's, as noted on the dyno graph.
So based on the numbers I gave you right above, you want to be in third gear to get the most thrust from a roll race at 65 MPH. Shifting straight to third is a bit much just because your engine has to climb 3000 RPM's in one shift. You can do it, but that's quite a hold on the throttle. But you're definitely not going to over-rev the engine, not even if you managed to shift to second. So if you get any staging time whatsoever, perform a few throttle-blip downshifts, THEN hit it.