I was thinking of racking to a secondary when it hits FG. Since you remove the fermentable wort from the bulk of the yeast I wouldn't expect to see much more of a gravity drop if you rack at 1.014. I would expect it to go to 1.012 but I've never needed to rack early nor have I tried it.
If bottling I would use a little less sugar expecting the wort to ferment a little bit more and the extra sugar would just increase CO2 volumes above desired levels. If it was my beer I wanted to finish I would bottle at 1.014 and sugar amounts to get me at the lower end of the CO2 volumes for the style. I'd rack to a secondary first though for a couple days them bottle. You will still have enough yeast to carbonate it may just need to stay at 75 for the full 3 weeks most people cite.
No, this would not work at all. The beer would absolutely not stop fermenting just because you take the beer off of the yeast cake. The yeast in the cake is mostly dormant anyway, and there would still be more than enough yeast in solution to continue fermenting just fine. If you bottled it with fermentable sugar still in solution, the yeast would just end up eating all of that sugar anyway plus the priming sugar. So you would end up with the same FG regardless and probably overcarbonation as well.
You should always encourage the yeast to fully ferment all of the sugar in the wort that they possibly can before you bottle. The solution to raise the FG is to put less fermentable and more unfermentable sugar in the wort. As many have said this can be achieved by mashing higher and cutting the simple sugar addition.