I'll cite Wookieepedia as my source, which if you look up Tantive IV it states it in it and all the citations are there. I believe though, specifically, it's mentioned in either the novelization or radio drama, and I'm quite sure elsewhere. I know a comic story arc revolved around Leia and her ship's crew even.
Actually after a quick look in just the EGVV, they state right in it that only Leia survives the ship and crew's capture, so there you go for a non-Wookieepedia one, haha. I'm pretty sure though their deaths were established as far back as the West End Games days, but those books aren't accessible for me to check.
It's on Wookieepedia though, which for a fictional universe is good enough for me.
I agree, it's quite subjective...
Timelines are subjective because the film is edited to speed things up, or at least one could easily assume that.
How you view Vader is subjective... I think a lot of your points are interesting about him softening up, but I just don't view him that way. His behavior at the end of ROTS, I feel, establishes his behavior largely till at least his encounter with Luke at Bespin.
I agree he's not one to sit back on the Death Star, but he was also pretty boastful standing on its bridge, since his plan led them to the Rebel base. He was pleased with what he'd just done to end Kenobi's life, and he was pleased that he could be a part of what he saw as the end of the Rebellion. I think him just standing there soaking it in shows he's pretty happy with the Death Star too. I see him as a man of action too. It's even mentioned that's why he likes Veers, that he leads the men into Echo Base himself... He's not a *****, for sure.
Still though, doesn't mean he dislikes the Death Star either... It's different interpretations of the character.
About the timing issue, a lengthy ammount of time between scenes isn't practical for the film. That's obvious. It's another fairly subjective matter. The only thing I think you can use as a gauge is the constant jumping about. Alderaan is blown up... I'm not a physics major, but it seemed spread out. Would it have been that spread about and things, without there having been a bit of time elapsed? Would it all already be cooled down and such? I don't know, of course, but it's another thing to consider I think, regarding time elapsed. Just as all the hyper jumping about for the Death Star and Vader are issues to consider. But there's nothing really solidifies it one way or the other.
I like to think there's a good deal of time there though, but that's just me.
To your three issues, I give you three counters that work for me explaining it the other direction...
#1 The Imperial prisons in SW lore are also something people escape from, and it's just natural that people will try. Vader's not a half-asser IMO, and so I see him being thorough and having no issue killing people, so anyone with any possible knowledge, no matter how small or unimportant, and even if they know something or not, are all gone. He wants it wiped out. If he doesn't, I'd think Palpatine maybe would, and he IS a prick even if Vader isn't. Maybe any survivor with any information would pass it onto other Rebels, or whoever, and there's absolutely NO reason to keep them alive except a softer heart. There's every reason to kill them, if just so you're mind is at ease (assuming Vader's a bit of a dick, of course).
#2 There's only zero risk, if there's zero information. Tarkin had the same thought that even if they had the info, nothing could be done with it. If he'd blown up Yavin IV, there's more Rebels than the ones there. There's a galaxy of a "billion billion worlds"... You only tempt fate by leaving survivors, at all, regardless of timelines or any other factor.
#3 Again, it's a galaxy of a "billion billion worlds". A small class of ship with a small crew, as the Tantive IV had, which a number were killed outright, are inconsequential to the Imperial war machine running or not. Some could hold secrets. I would think they're kept as long as they felt was necessary, however, Vader chokes the senior officer to death. I don't doubt some are kept for a while, but I think by the time Leia's death order is given, they're already dead. Interrogated and exhausted of information. Any information they were holding out on, especially regarding the new super secret ultimate weapon thing that cost a lot, is going to go with them, and not be useful to anyone. That to me far outvalues a Rebel soldier's usefulness as a slave, or even a sleeper "manchurian candidate" type situation. Ultimately you have the Death Star now, and if you've secured its secrets, you wouldn't even need such an elaborate scheme.
I totally see your points, I just don't agree is all. It's an impasse, but not one without seeing what each other's points are anyway.