With regard to not noticing a missing planet, if they knew Ceti Alpha VI was their destination, and they plotted a course to there, apparently finding it where it should be, would they really have been counting planets? It someone charted a course to a specific Caribbean Island, and had never been there before, would they notice if another island just happened to have gone missing?
Again, Earthbound analogies don't work in space. Earth has horizons, so you're only in the direct line of sight of things that are within a few kilometers. In space, the whole universe
is in your direct line of sight. Sure, you need a sensitive enough telescope to see most of it, but Starfleet vessels have great sensors, and it stands to reason that they'd be scanning ahead to get an overview of any system they neared, especially if it were largely uncharted. Heck, at the very least they'd want to scan for navigation hazards like, say, a huge cloud of debris from an exploding planet.
And as I've said two or three times before, light travels at a finite speed. If the explosion happened fifteen years earlier, then as soon as they came within fifteen light years, they should have actually seen the planet blow up. The sensors should've detected a massive disruption/energy release in the system and alerted the crew. Basically the story as written only works if the Reliant
is the 18th-century sailing ship Meyer wanted to pretend it was, a primitive wooden vessel with no sensory capability beyond the crew's eyes. It doesn't make one damn bit of sense for a 23rd-century starship.