I think when the pot is sitting lower in the cone the net effect is that less oxygen is available for the combustion process. This will certainly slow down the burn time. In the worst case scenario, if you're alcohol stove is oxygen deprived, you will not get a complete combustion. The result is a "cooler" burn with Carbon Monoxide being a significant resultant along with Carbon Dioxide and Water Vapor. The Trail Designs stove has been "tuned" to be used with the cone. I believe this tuning is dependent on the size of the aperture in the middle of the stove + the size and number of the intake holes in the stove + the size and number of intake holes in the cone. Thus reducing the amount of oxygen going into the cone ( that's what you're doing when you lower the pot into the cone too far ) without reducing the aperture size on the stove could result in excessive carbon monoxide and a less efficient burn.
1) To use the cone without the stakes, you should reduce the aperture size of the stove. This can be done a number of ways. The way I did it was to get the top off a tin can and cut a small triangle in the middle with some tin snips. Then after lighting the stove and it's going nice and strong, place the damper on the top of the stove. Note: I have seen the stove go out more often like this, and the heat wasted from having to re-light and open up the cooking environment didn't seem to justify the fuel savings. Additionally it was one more bit of gear to remember to pack up and one more little thing to get lost and forgotten about at camp.
2) If you're looking to save a few grams by ditching the extra stakes, I had good luck bending the stakes into an "L" shape and removing the extra material from the end. This reduced the weight of the stakes by about 1/4 and the stakes stay in the cone easier due to the "L" shape. In addition, I trimmed the priming tray off my 12-10 stove so it is more easily stored in my cook pot. The stove has gotten a little bit "dinged" up. But it still works great.
I believe that Trail Designs has done significant testing to determine the best balance of fuel consumption vs. cooking times. I spent a lot of time re-doing their work only to discover that Trail Designs did it right. Don't get me wrong, I had a great time playing with the stove. So if it's fun for you to experiment, then have at it. But my experience is that the height of the pot, the holes in the stove, and the aperture size are absolutely perfect as is.