Pike orders Chekov to give mission broadcast. Which usually is given after the ship has began it's course. Not several hours later.
In this situation, it could have been after pertinent facts have been sorted out, though. Chekov does reference supposedly confidential Starfleet communications intercepts, combining two that at first sight do not appear related to each other in any manner; this after a really hurried departure during which not even the senior staff aboard most ships might have known all the facts yet.
That gives us the excuse to go for a multi-hour journey - beneficial not merely because it would be more consistent with other takes on the Trek universe, but also because the journey to the opposite direction, from the erstwhile Vulcan to Earth, takes quite a bit of time. Or at least it takes Nero an eternity in terms of plot events, and our heroes only barely outrun him to Sol.
it took 72 advanced torpedoes exploding inside the ship to actually disable her, which is a testament to how rugged that ship is.
Let's remember, though, that those were "fake" torpedoes. Perhaps after Khan's modifications, there was enough warhead material left for matching one standard torpedo? Or as you say,
Weren't the warp capable torpedoes lacking the initial warheads though?
The thing is, our heroes didn't know what was inside and what wasn't, so the dialogue isn't helpful here. Carol Marcus obviously thought that when the torpedo was triggered to start a countdown to explosion, said explosion would be large, but she may have been totally wrong. She was an expert on the weapons as designed, after all, not as modified by Khan - possibly a blinding fault.
Another thing Khan may have left on the pier when modifying the torpedoes is the ability to fly at warp, or even at sublight. After all, if it ever came to Kirk actually firing the torps, Khan would have lost the game, and he isn't the sort of a guy to plan for defeats.
IIRC, the first hits she sustained made her basically combat ineffective insofar as putting up a fight, i.e., if she decided to stay put and slug it out, she'd be dead. The captain of Kelvin obviously thought such.
Interestingly, the Kelvin
lost weapons capacity twice during the first fight, and regained it pretty quickly - once during the fight itself, and once between the fights. Incapacitation of the ability to fight back probably didn't feature much in Captain Robau's decisions, then. He would have had to be thinking in terms of not withstanding Nero's pounding defensively, or
in terms of the Kelvin's
weapons being impotent offensively in the first place, even when undamaged. Which may well have been true, as we never saw her weapons hurting the Narada
in any way. The mining rig did have shields of some sort, mentioned in dialogue, even if those did little good in subsequent fights.
Why Pike would think his ship couldn't resist more of Nero's torps at Vulcan, we don't know. Sure, Pike's shields were weak, but later on we learned his ship can shoot down torpedoes. Indeed, he gave the command to prepare to fire all weapons, despite having suffered the initial hit. Quite possibly his decision to surrender to Nero stemmed from strategic thinking unrelated to the actual vulnerability of his ship... The shuttle journey did give him two advantages: the sapper team on the drill, and a delay while Nero tortured him.
That in mind, Nero's shield-shattering first hit might in fact have been fairly insignificant and not the sign of great offensive power in practice.