The fact that Destiny is a moving object which apparently has a static gate address (which I think other shows have determined wasn't possible, or at least not feasible) makes me think that perhaps the ship was meant to be staffed the way it was staffed just now. Maybe it was meant to start off unmanned and its crew would join it while it was already near its destination.
To carry on your observations, there was also no sign of real furniture (for any humanoid type creature) aboard ships. Something I forgot to mention earlier. Walk on any human vessel and furniture is immdiately obvious most places. Especially at command and control centers. People have to sit and monitor and on vessels meant for long term missions, sleep and eat.
Leading me to one of these conclusions. 1. There was never any intention for the ship to be occupied for long periods of time, but rather to be visited intermittently and then abandoned again until the next necessary moment. So no real need for furniture. 2. The furniture has decayed over time, but in a hermetically controlled environment this seems highly improbable - that furniture would have been constructed to intentionally decay over time or that it would be constructed so differently as to decay when other things don't. 3. The furniture is designed to be hidden or regressed when not in use. 4. The furniture was removed when the ship was last abandoned (That is they carry in and remove any unnecessary supplies or goods, which might be explainable by power consumption rates). 5. The furniture was removed by a third patty or someone who found the ship other than the creators/users - this seems possible but unlikely to me unless the third party also removed other things on the ship, modified the ship, or perhaps even sabotaged the ship - it's possible the scrubbers were sabotaged or over extended themselves trying to compensate for losing atmosphere..
My assumptions are that nos. 1, 3, and 4 are the most likely possibilities, with 1 and 3 being my likely favorites. Because the ship has an atmosphere and obviously has controls for necessary human interactions, but no apparent furniture. Meaning no long time or long term crew-interactions. Also I would think that the life-supports systems would operate at null or bare minimum capacity when the ship is not occupied. Meaning to me that the ship was recently occupied, the crew was recently forced to abandon ship, or the ship itself was anticipating occupation, hence the available atmosphere. Meaning it is also possible that the ship either anticipated the arrival of the current crew (the humans) or life support became active immediately once it detected it had been dialed from the outside. But the time frame for that would be short indeed because not only must you compress atmosphere but you would have to generate a lot of heat (heat any occupiable area of the ship). In a space between galaxies or between stars and in motion you couldn't rely upon outside energies sources for much or any supplementary assistance. Meaning that the ship, if it had anticipated the humans, would have had to have done so long before being dialed to bring up enough atmosphere, enough heat, etc. to be useful.
Also one has to consider that they have explored very little of the ship and the ship may not be totally abandoned but has a small reserve crew, possibly in stasis or suspension, or attached to some area of the ship they cannot yet detect or have not noticed.
The fact that it dropped out of FTL once it was instructed by Rush of the situation makes me think that it is indeed at least partially artificially intelligent. And that it was indeed designed either to emplace or scout for Stargate addresses, or to reach destinations not reachable by Stargates.
Implying one of two possible missions (maybe both, maybe something else, but probably similar). Colonization throughout a cluster of galaxies, maybe any entire section of the universe, and/or exploration well beyond the home galaxy, and to the information to which that might lead.
I had a moment, too, when I thought the flying cameras (what did they call them? Kenos?) might be used to close the door to the shuttle, but I have a feeling that the cameras can't be controlled delicately enough to push a button. Maybe they're even designed not to collide with objects, so it would've been impossible to make it interact with any controls without taking it apart and doing some re-engineering, which I doubt they had time for. Making the cameras so that they detect objects and stay X inches away from them seems like a very valid safety feature to build into a flying sensor/camera.
In any case, I agree that they should've at least mentioned the possibility of using the cameras. You'd just need ten seconds of dialog: "Can we use the cameras to close it?" "No, they can't push buttons. I can't get them to go within six inches of a solid surface. I think it's a safety feature."
I thought of that myself. They're spherical (covering at least, the internals may be reconfigurable) making pressing a button on a flat panel nearly impossible (considering the control panel size and the camera size). But they could have tried tying a pen, a pointer, a magnetic arm, etc. to the sphere (as an extended arm with which to press the button), assuming it was not frictionless, which it may have been. It's all moot now, I would tried it, but it was nice to see a Senator actually do something selfless and productive for a change. So, I'm not complaining.
I think they called the floating cameras Kinos by the way, after, I'm assuming either
this, or
this, or
this. All deal with cameras, lighting for video production, and recording data.
Anyway, nice observations.