About the lone Stardestroyer idea, and the in universe reason for it being there… I’m thinking it’s there to oversee the area, making sure nobody escapes with the droid, and to direct troops and TIEs below. Fair enough, seems logical.
But if it’s there and everyone sees it’s there, there’s no need to hide anything. Assuming Kylo is on this Stardestroyer, it would make sense for him to as soon as possible go for Rey and BB8. Why wouldn’t he fly out of this Stardestroyer rather than appear from nowhere later?
It also makes everything more relatable for the audience. Instead of asking why the Stardestroyer is there and who is on it and what is the point, they can see that it brought Kylo. Everyone knows Kylo and what he wants and what danger he represents so everything is made (seemingly) clear, logically and emotionally.
But sending out Kylo also hides the other, hidden purpose, which is the large scale attack, both in universe and to the audience. To me, seeing Kylo and him actually moving toward the heroes (as opposed to a ship just floating above) gives a bigger impact than a nameless Stardestroyer with an unknown mission.
If you don’t agree, of course I’ll help with whichever scenario you prefer.