The island existed in time & space. no specific point as it could be moved. How, i have no idea.
The golden light was the "heart" of the island. Put out the light and the island goes to hell, thus the world ceases to exist. Jacob explains this in season 6 using a bottle and a cork.
The polar bear was brought to the island by the dharma initiative, season 4 or 5 i think its referenced
The numbers were shown in season 6, when Jack and hurley went to jacbos light house
Pressing the button contained the energy/light. how, again i dont know.
Jacob and richard staying alive for many years, not a clue
Chinese dude hearing dead people, same as sixth sense. some people have a gift.
Island time travelling, not a clue. I think that was explained in part by eloise hawkin in either season 4 or 5.
Widmore needed desmond due to his resistance to electromagnitism. How, again, not a clue. Same goes for why is desmond so special
Heres a good link i found on talk audio
http://screenrant.com/lost-finale-explanation-kofi-61464/
might explain more than i have or even can.