On the Executor commentary - yes...they do have a backup bridge / engine-room etc. onboard the command-ship.....BUT....as one of you noted earlier, the fact is...the impact, explosion, and loss of helm control / engines / etc. happened so suddenly - that there was ...what...1-minute ? - mabye less ? - for the crew to react and do anything...and they were in the midst of being peppered from heavy fire from all surviving Rebel capital ships (I think the Rebs had 2 Mon-Cal Cruisers still left at that point, plus several frigates and light cruisers, and several hundred fighter craft too - so Executor, mighty though she was, was really getting the crap kicked out of her).
And the key as to "why does it sink down ?" - is, as someone said, that the Death Star's gravity was so intense, it rapidly pulled the massive ship into it - remember the DS-II was even LARGER than the 1st Death Star - I think the canon-numbers listed for DS-II are 160,000 Km - across (total circumference) - that's appx. the size of the state of Ohio in the USA. So look at a map of US...look at Ohio...and imagine a big globe / circle laying completely over the state and coming off the sides of its borders by a bit. That's how big the man-made Death Star II was !!!!!!

So the gravity for that thing, was quite monstrous - esp. when the Executor was in such close-orbit of the station to begin with - it didn't really have far to "fall" before impact and complete destruction.