Most likely not in "The Ultimate Computer" - 400 members of the Enterprise crew had to leave the ship.
Yet this very feat was achieved in emergency conditions in "The Doomsday Machine", explicitly with transporters.
That is, unless Decker lied about this rather unlikely twist of events...
Remembering the queues in "This Side of Paradise" they probably got faster off the ship by doing it the old way.
But that was a bunch of mutineers abandoning not just the ship but all discipline as well. And being in no hurry.
In "11001001", the E-D with its explicit 20+ transporters was clearly benefiting from the availability of a physical gangway when evacuating up to a thousand people. But this was done in minutes, and Kirk would have had hours to offload his personnel. Then again, Kirk's ship would sport an explicit gangway after the TMP refit, and there's no good reason to argue against
the use of such a means of disembarking in TOS.
At most, it could be argued the gangway would not be on the saucer rim, because we see no evidence of it there, and that a staircase or ladderway (and/or turbolift connection) through a dorsal hatch is the likelier means, just as you postulated.
What if there are technical difficulties with the transporter?
Then people freeze to death.
Would physical means of disembarking be a "contingency plan", a "primary means", or perhaps "Plan C if both transporters and escape pods fail"?
K-7 may be serving a purpose it was designed for: to harbor valuable cargo until it can be either processed or traded or simply picked up. It could be a standard use for stations like this. This would seem to be backed up by the station's obvious personnel uses: shore leave, shopping/trade, a platform for official business, etc.
The curious thing is that the readiness for such operations includes grain silos
. What else is waiting in the wings? Pools for genetically enhanced shrimp? Storage racks for Douglas firs? At some point, diversity and capacity would start competing, and the station would either lose the less likely capabilities, or then have insufficient capacity for each capability.
If such a station were located in orbit around a planet or moon, how difficult would it be for a station of that size to keep the orbit from decaying?
Good question. Terok Nor, a decidedly planet-tied station, wasn't exactly on "low" orbit, and would have experienced little air resistance at the apparent height of perhaps a thousand kilometers. It was generously provided with thruster capacity, though - and Cardassians seemed to have dedicated a lot of effort to sabotaging that particular system when they abandoned the station, perhaps in hopes of having the station crash.
K-7 doesn't have obviously visible thrusters. But the thing is, neither does Kirk's ship!
(But if your station is using transporters and subspace transmitters all the time, wouldn't that kind of usage demand the same kind of power generation that a starship uses?)
Are those high energy systems, though? We never quite learn about transporters - but they seem to work in rather fancy situations, such as when all power supposedly is shut down yet Dona Ragar manages to fire up a platform by using a hand phaser battery. And "terawatt" communications amaze Riker in "The Dauphin", yet the main power systems of his starship appear capable of significantly greater power output, perhaps indicating that communications in general don't require all that much power.
When our heroes in "Tribbles" approach K-7, Kirk asks how close the course will take them to "the Klingon outpost". This sort of suggests that the Klingons have a direct counterpart to K-7, with both stations quite possibly dedicated to the same task, namely, staking a claim for this "disputed quadrant".
Of course, it may also be that K-7 is
the "Klingon outpost" they are talking about, and that's what the K stands for there. When Chekov speaks of smelling "them", he might not be making a racist remark after all, merely a generally humorous one.
When Nilz Baris takes charge, he is taking charge of the Sherman's Planet project. Kirk seems to think this should in no way be connected to placing the entire quadrant on alert. But Sherman's is the only quoted point of conflict in the quadrant in Chekov's analysis... All the dialogue might be taken to indicate that Sherman's is the raison d'etre of K-7.