...the USS Enterprise, right?
Well, sort of. It was a supercarrier and the heroes called it the
Enterprise and the gangway leading to the ship read "
Enterprise CVN-65", yes. But it didn't look like the real
Enterprise, CVN-65 - it looked like the ship that was actually used for the filming, the non-nuclear
Ranger, CV-61. Which is funny, because we know that in the 22nd, 23rd and 24th century, people in the Trek universe will believe that CVN-65 looks like the real-world CVN-65, and have the artwork to prove it.
I guess the ship underwent a refit at some point, and is memorized in history in one guise while seen in ST4 in another. All that differentiates CN-61 and CVN-65 externally is the "island", the superstructure looming above the flight deck, and CVN-65 has a distinct shape because there's an antiquated radar system there that has this boxy antenna structure. In the Trek reality, it's quite possible that the Navy decided to invest in removing that relic and installing a more modern, hence more conventional island shape there; in our reality, the Navy has simply retired the ship as is.
I do not know if stealing neutrons would affect other peoples lives
As far as current scientific knowledge goes, it's complete nonsense anyway. If you can trap neutrons in your fancy pocket doodad, they won't be any different from the neutrons you get from the nearest rock or bush or seagull - you don't need a nuclear reactor to get them. But even in the Trek version of physics, clearly the heroes are only pocketing neutrons that are already flying out of the reactor (and hence perhaps decreasing the cancer rate among the crew but not affecting much else)...
Whereas using counterfeit money to buy material from a company would have some affect on the economy and the future right?
Probably less than stealing or renting that helicopter.
On topic: Given how callously our heroes treat property in the general case, I don't think they would make a big fuss about offices or cabins or the like. Kirk might have an office, he might requisition one as needed, he might simply tell another officer to take a hike; in terms of technology, his office would probably be carried in his pocket, in one of those memory cards, and he could use any of the interchangeable cabins for actually doing the "paperwork".
Timo Saloniemi