I'm not sure what you mean by the long corridor forward of Main Engineering.
http://movies.trekcore.com/gallery/albums/tmp2/tmphd0430.jpg
The corridor from which Kirk is arriving runs from bow to stern, both in terms of how the set was built and how it was photographed. It truncates at the front "pressure door" of Main Engineering. To add insult to injury, it is also extended by a matte painting, as can be seen - poorly so, giving the "floor" an upward kink where the matte begins.
But it
is eminently logical for Kirk to reach Main Engineering from this direction: he has recently been to the Main Bridge, which is upward and forward of Main Engineering, and a vertical turboshaft coming from the saucer would logically run along the very forwardmost path available in the neck. (Perhaps this shaft is what we see highlighted in light green on the hull paint, now that it cannot be the intermix shaft?)
There is no crystal on the NX
Sure there is.
http://www.trekcore.com/gallery/albums/nxenterprise/NX1.jpg
In terms of blue glow, there might even be three - two more atop the booms, at the "turbochargers". Although those were usually not intended to glow.
Well, there are four round things per side that glow dim blue.
http://trekcore.com/gallery/albums/ussdefiant/firstcontact0135.jpg
In ST3; in ST6, she has changed for two smaller ones. Both versions of the ship are witnessed performing various TNG and DS9
Excelsior class duties, because some early stock footage was filmed with the single crystal, while later shots used the modified model. The smaller model built for VOY uses the two-dome configuration, as does at least one CGI model.
and it can still be part of the warp intermix system (which in the movie days, doesn't seem to need to be a straight line like the TNG days)
Oh, most definitely. Although in TNG, the "shafts" tend to be very short even if ramrod-straight, and therefore a TNG style arrangement would be fine for ST:TMP as well.
The crystal's purpose being something to do with moving power from the warp system to the impulse system.
Or then not.
Scotty also needed a bit to get those batteries to fire the phasers. As Decker said, the phasers automatically cut out when the warp power goes out. That doesn't mean they can't bypass it, but that takes time.
Only in TMP. And firing phasers when warp is out for the count has always been possible in all of the shows, starting with TOS; it's an exotic quirk of the first movie only that the ship would have any sort of a limitation in this respect, and it logically should be corrected ASAP by Starfleet engineers.
Scott is very experienced with bypassing systems and has a cadet crew that has been learning all about they systems, so they are up to speed on things. Kahn's crew is inexperienced, and untrained. It would take longer to get their phasers back online, giving Enterprise time to rough them up even more if they stayed. They do repair it later over Regula before going to attempt an intercept on Enterprise (after getting the Genesis device and leaving Kirk behind).
I wouldn't credit Scotty's cadets with the ability to straighten a bent paper clip. OTOH Scotty would have a dozen things to worry about after Khan's first shots, rerouting of phasers possibly not being much of a priority (because the skipper keeps yelling for SHIELDS, not weapons, and there's a big hull leak and whatnot).
It's theoretically possible that both ships lost all weapons capability for a moment. But neither crew comments on such a thing happening, and this is not something required by the plotline or the background treknologies.
Timo Saloniemi