Between TWOK and TSFS things about the bridge changed.
To be fair, as Kirk said "the bridge [was] smashed" so in the long journey home where they picked up twice as much damage to the hull (
) they probably replaced a lot of stuff with spares.
Yeah, possibly. The time span between the two films has always been kind of cloudy so we don't know just how much time the battle-worn crew had to make some repairs with existing stores of parts.
The only thing we know for certain is that Saavik and David had enough time to transfer over to the Grissom and arrive at Genesis to begin their scans and studies, but that doesn't require all that much time given that starships can travel at high warp and the request by Saavik and Kirk's son to go back to Genesis aboard the closest available science vessel wouldn't have taken long at all to get the greenlight.