Coil and turns is one of the same. Coil of bahumut is comprimised of i believe 11 turns in total now.
There is first coil which is turns 1-5, second coil known as scob which is 6- 9 (maybe not sure as i have not completed second coil yet) and then 3rd coil.
You first unlock coil through the main storyline and no it is not the end of the game per say. Expansion is coming out Spring 2015 after all.
Each coil does have certain gear level requirements in order to enter. If you do not have soldiery gear yet at level 50 you can run Syrcus Tower to get that gear first.
Also to note each turn except for turn 3 drops items, turn 5 drops weapons for example. Hope this makes a bit more sense to you now