Why does it take the Federation two months to do anything about the explosion on Praxis? [Because (as we see in the first ten minutes of the film) the prideful Klingons didn't want anyone entering their space.]

This might be subjective, but why does the Enterprise take so much damage, especially interior damage, long before the shields actually collapse? [There's a limit as to how much the shields can protect the ship. Depending on the force of the explosions, the ship still suffers some damage from any weapon blasts. Also, the shield only holds for so long and gradually loses it protectiveness with successive attacks, causing increasing damage to the ship.]

Is it my imagination, or does the opening theme sound similar to the classical piece "The Planets - Mars" by Holst? [There are certain similarities, yes. Whether any specific aspects of the piece were deliberately incorporated into the film's opening theme is an open question, but the overall feel is undoubtedly very similar.]

I don't understand why Spock insists that the magnetic boots must be on the Enterprise and not on the cloaked bird of prey. Spock points out that someone involved in the assassination conspiracy must be on the Enterprise, because this person must have altered the data banks. I agree with him. But why does that prove that the assassins who boarded the Klingon ship must have beamed from and returned to the Enterprise? How can he assume that the assassins and the computer hacker are the same person/people? Maybe there are assassins on the cloaked bird of prey and only a hacker on the Enterprise. Or, maybe the assassins might have beamed from the Enterprise but then carried on to the bird of prey, once their work was done, instead of returning to the Enterprise. And finally, if Spock does think the assassins beamed to and from the Enterprise, why is no one looking at transporter logs/records for evidence of unauthorized beaming to Kronos 1? [It's fairly simple - somebody good enough to hack the weaponry databanks on the ship would undoubtedly be able to alter the transporter logs, so, while they were undoubtedly checked (we do see Chekov investigating the transporters - he would certainly have looked at the logs), they'd be unlikely to glean anything from them. They'd also be good enough to cover their tracks, so they're not going to get very far investigating the computer breach. As such, the only specific thing that they can look for are the gravity boots - this does make the assumption that the assassins came from the Enterprise and returned to it, but, at that point, all they have to work with are theories. However, while the only specific items that they can look for are the gravity boots, the search might also turn up other items that could indicate complicity in the events on Kronos 1 - the hacker probably used some specific computer tools which could be found.]