A space faring ship divided in two primary structures, designed to accommodate between 9,000.00 - 12,000.00 individual humans in a
conscious and active state at any given time.
The first structure houses essentials for sustaining life and provides these to the secondary structure, where the humans are
housed. They are attached to one another through key pivotal points.
Fine so far.
The secondary structure is a planet-like sphere approximately 900.00
kilometers in diameter. It rotates at a high speed in order to create
That's pretty near the edge (and on the "too big" side of it) of what reasonably foreseeable materials technology can handle if you want 1g of apparent gravity.
However, you don't specify precisely what the relationship is between this second section and the first. If the first, non-inhabited section surrounds the rotating section, an does not itself rotate, then it can provide additional structural support (with force transferred between the sections by rollers or magnetic bearings), which could make such a structure feasible. The bearings would require maintenance to last for thousands of years like you want... but you will already need bearings on the polar connections between sections, which will themselves need maintenance anyway, so this isn't any new restrictions that weren't already there. Additionally, if the uninhabited section surrounds the inhabited sphere, it can provide radiation shielding which would then not have to carried by the sphere itself, reducing the load.
Finally, note that if the inhabited section is in fact spherical, you will only get 1g in a narrow band around the equator. That's also the only area in which the ground will actually be near-perpendicular to spin gravity. If you want to maximize the actual inhabitable space, you either need to terrace the sphere, or make it a cylinder instead--and if you want 1g everywhere, then you have to make it a cylinder.
and counteract the speed at which the craft travels, which is 32% the
speed of light in a single direction (95933586.56 m/s), such that the
effects of this speed will not be felt by the occupants.
This is irrelevant. The only effects of speed that might matter are induced radiation; spin will do nothing to counteract that, and in every other way the inhabitants would have no way of telling how fast they are moving with respect to the rest of the galaxy.
The ship is designed to travel for at least 21,000.00 years. The ship
and human technological capabilities is based in a time between 150
and 250 years from the current year (2017).
As long as the inhabitants realize that they will need to do regular maintenance, that shouldn't be a problem. Moving parts, however, just won't last anywhere near that long, and neither will solid-state electronics--the doping materials that make them work will slowly diffuse out of their functional positions.
The ship is equipped with the ability to create and sustain magnetic
fields that are 'multi-spectrum' i.e. capable of affecting (attracting
and repulsing) some materials that are not ferromagnetic.
That just sounds like magic. Magnetic fields can indeed attract and repel non-ferromagnetic materials, via diamagnetism and paramagnetism, but magnetic fields don't have a "spectrum", and it's not obvious what purpose "attracting and repulsing some materials" would have. It is, however, a decent idea to surround the ship with a large magnetic field to act as a radiation shield (against protons, beta rays, and alpha rays).
its maximum speed in relation to spin of the secondary structure etc.
There isn't one. The speed of the ship and the spin of the inhabited section have no relation to each other whatsoever.
If it is the case that this is possible, then how would each aspect
need to be balanced if I want to prioritize speed over any other
factor (population size, longest possible travel time etc.)? If this
is not possible, what is the closest alternative that is similar to
the suggested concept i.e. a self-sustaining man made biosphere that
can travel at a high-speed in any one direction for more than a
If you really want to prioritize speed over any other factor, this is clearly a terrible design. To maximize speed, you accept that your population will have to be zero, cut the ship down to a thin reflective sheet with embedded electronics, and launch it with a laser powered by a Dyson sphere.
But that's almost certainly not what you actually meant.
If you want it to last for thousands of years, it will need to carry a population to perform maintenance, and it will need to carry all of the industries needed to create and recycle its own parts so as to carry out that maintenance. So already, it needs to be fairly large and carry a large population, and you wanted a large population anyway, so that works out just fine. At that point, you have to ask "OK, I've got this huge ship--what do I have to do to accelerate it to .32c?"
There are lots of possible answers to that question, depending on important follow-up questions like "does it have infrastructure at the launch site to help it accelerate", "does it need to slow down again at the end?" and "if so, is there infrastructure at the end to help it stop?" Some deceleration can be accomplished with a magnetic sail, which can be included as part of the magnetic radiation shield that you might want anyway; that won't be able to stop the ship on its own, but can help reduce the magnitude of any other deceleration systems.
If you have infrastructure at the launch or destination sites, the ship could be accelerated / decelerated by laser sail or mag-sail. If not, the ship will consist primarily of fuel and reaction mass. If it only needs to stop itself (or start itself), but not start itself (or stop itself), then it will be mostly fuel and reaction mass. If it needs to do both, even with a passive mag-sail assist, the ship at launch will be mostly the fuel and reaction mass needed to accelerate--and once it's up to speed, what's left will be mostly the fuel and reaction mass needed to decelerate, with the 900km-wide habitation sphere appearing as a tiny speck in relation to the gigantic fuel tanks. Additionally, it will be nuclear powered--either fission or fusion, or some futuristic mass-energy-conversion technology. There just isn't enough chemical fuel in the galaxy to accelerate a small-moon-sized ship to one-third of light speed.