a) Kirk never informed Starfleet he dumped off a bunch of dangerous hijackers - including a fellow crewmember - to some barren planet. Kirk is known to bend the rules for a positive outcome, but something as flagrant as all this?
Kirk tends to protect people he approves of, including many of his adversaries, going as far as hiding the very existence of such people. He lied to Starfleet about Zephram Cochrane (that is, he never told he met the guy); he lied to Starfleet about Gary Mitchell (that is, he claimed Gary was doing his duty when dying, when in fact Gary was an outright adversary and traitor). He probably also left Flint the Immortal die in peace rather than squeal on him - a recurring motif there, as Cochrane was also going to die (by Kirk's actions, if indirect - due to those, the Companion had chosen to cease to be a fountain of youth for him). Letting Khan perish on a harsh world would only fit that pattern where Kirk in theory has no blood in his hands afterwards.
Since Kirk tends to dictate his logs well after the fact (there being no chance of doing it while the events unfold, plus he says things like "unknown to any of us at this time" in 'em), lying about stuff is pretty trivial for him. He's also one of the three people officially acknowledged as capable of forging records, as per "Court Martial", and while Spock might do it because he's a computer wizard, and Ben Finney because he's a computer wizard
and the Records Officer with all the clearances, Kirk probably can do it only because he has all the top clearances.
And Kirk did approve of Khan. Depending on which sources we trust, Khan might have been a hunted war criminal, or merely a deposed dictator; Kirk chose to dine with him, and confessed to admiring him, too. Scotty felt the same way, and McCoy was willing to join in on (what soon became) the joke at the expense of Spock who strongly disagreed.
Kirk would thus probably meet divided opinion if he exposed Khan to the broader public, too. So he quite possibly chose not to (as even Spock's angle here had been that the people did not want to know), and then forged a few records.
Contrary to common fan interpretation, nothing in "Space Seed" suggested that Kirk would plan on visiting the colony one day. Quite to the contrary, Spock speculated idly on the possibility of such a visit happening, presumably centuries hence, against the apparent default assumption that Khan would be left to his own devices and never suffer from observer effect.
Ceti Alpha VI exploded and nobody knew about it (which seems odd as they have star charts)
They only have star charts if a starship goes places and makes those. Planets exploded in "Doomsday Machine", too, and the only way to find out was for a starship to bump into the rubble - again and again, system after system, as our heroes followed the path of the thing that blew up those planets.
... then again, how did Khan know it was the neighboring planet and not something else?
As per the above Trek precedent, nobody would see Ceti Alpha VI blow up from a distance (at least not until hundreds or thousands of years later when the light of the explosion reached a Federation asset). Khan might see this happen with a telescope set up on CA V, though. Or then he'd deduce that the explosion happened, and he might be dead wrong for all we know; the heroes themselves never get to put a word in edgewise, or to conduct an analysis.
Did Space Seed specify the number of planets in the system as a base point?
No. But what difference would that make? Counting of planets is a chore: if an Earth space probe entered our own star system, it really couldn't tell whether there were any planets here at all initially, and even after a careful study, nothing about "Oh, now I have seen five" would tell it either "There must be more to go" or "That's all, folks".
(Space Seed has Spock opining what it might be like in 100 years if a ship came back to see what Khan made of the place... so what did Kirk write in his logs?
Well, he conducted an official inquiry, which included both Khan being cleared of all charges Kirk might have held against him - and Khan being given a planet to live on. He'd either have to delete the records of that inquiry, or then tell his like-minded superiors to bury the records so that the public would never find out. And he'd then have to do another Gary Mitchell and pretend that Marla McGivers had perished/disappeared in the line of duty, rather than betrayed everybody and eloped with the villain. But all that is right down Kirk's alley.
Or Spock, do all command officers say them only if they're filling in for the captain?)
Well, the only time we hear of Spock (or any other top officer hero) being disloyal to Kirk in this respect is ST:ID. Quite possibly, whenever Kirk announces over the PA "From now on, red is going to be green", there isn't a single crew member who'd dare or wish to disagree.
A ship would, when entering a solar system, scope out planets.
No, she wouldn't. "Doomsday Machine" is an excellent example of this. Ships don't care about planets, especially if they have maps of the system. So what happens is that they occasionally bump into the rubble of a planet and at
that point first start scanning.
Scanning for the absence of a planet is a non-starter anyway. How could scanners tell that a planet is missing if they see nothing there? About 100% of space is
supposed to be like that.
In TMP, they did say they couldn't go to warp while in the solar system.
...Because they had untested engines (ones that did go kaboom on them in the end). Before TMP, that is, in TOS, not only had it been trivial for Kirk to go to warp within systems - Scotty almost had a stroke when Kirk suggested they fly inside a system at mere space normal speed in "Elaan of Troyius".
Even with those untested engines, Kirk felt happy buzzing Jupiter at point blank range. Perhaps because he thought that if he did blow a gasket, it would be nice to be very close to a civilized planet? Buzzing of planets only happens with deliberation, though: you can't accidentally hit a planet even if it isn't quite where somebody else's haphazard space maps suggested it might be.
Reliant's crew didn't do enough research into the logs before heading on out to Ceti Alpha V, thus being oblivious to "one of our planets is missing", the fact people might be there, and so on.
It's clear the system wasn't flagged with "Khan Here, Beware", yes, and that even in the best of cases, discovering this would involve some digging. And it's unlikely the crew would do any research on the system, because what would be the point? They only wanted their desert planet. They went looking for it, and found it, and it didn't matter to them whether it was Ceti Alpha V or perhaps Tau Kappa ½.
They certainly couldn't have trusted existing logs on the matter: if such logs described the CA planets in detail, the ship would have no mission, and Carol Marcus would have found her desert planet simply by sitting down at the library computer with a nice cup of tea.
Timo Saloniemi