I can't find any information about that on the web so here I go :
What will happen to the resolution if I mount a DX optics and shout a video? Will it stay in 1920*1080? Or will it be cropped to some random resolution?
The D800 can record "full HD" (1080p) and "HD" (720p) 16:9 video, regardless of the lens attached (FX or DX). The resolution will not be reduced, because the D800 has plenty of pixels to spare, even in DX mode. However, the field of view will reduced by the crop factor, just like it would be with still photography.