'why it stays balanced? that is easy the amount of mass loss due to burning the toothpick in negilble (spelling)'

The odd thing is that the forks will even sit on the rim of the glass in the first place. While the mass of the burnt away toothpick is negligible, the center of gravity of the whole fork/toothpick mechanism must lie directly over the point where the toothpick meets the rim of the cup somehow. Possibly due to its fulcrum.

'why it stops? the cup takes heat away faster than the wood burning generates it, when the heat drops too low
the wood cannot be self sufficient in combustion'
It's like how you can boil water in a paper cup but if you put the paper cup over same flame empty it burns'

When I first saw this I thought it was correct, but if you check a few links below the video posted you'll see the same thing happen with a glass cup full of air. Glass is a very poor conductor of heat. Therefore I can only hypothesize that while there is some transfer of energy flame to the cup, the reason the flame goes out is because there is not a free movement of oxygen around the flame at the point of contact with the cup and as flames burn upwards the lack of oxygen at this point will cease the propagation of the fire. Hence the flame will still burn a little on the top of the toothpick when it reaches the cup but abruptly goes out.