[hamdani yusuf (OP)]

Here is what wikipedia says

The Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized. Thus an atomic-scale system was shown to have intrinsically quantum properties. In the original experiment, silver atoms were sent through a spatially varying magnetic field, which deflected them before they struck a detector screen, such as a glass slide. Particles with non-zero magnetic moment are deflected, due to the magnetic field gradient, from a straight path. The screen reveals discrete points of accumulation, rather than a continuous distribution,[1] owing to their quantized spin. Historically, this experiment was decisive in convincing physicists of the reality of angular-momentum quantization in all atomic-scale systems.

What would happen if the magnetic field used is homogenous? What would happen if the magnetic field used is only slightly inhomogenous?
If the source is contaminated with particles with zero magnetic moment, what would be the result? Will it interact with particles with non-zero magnetic moment?

In the animation, starting from 0:25, why the moving magnets don't rotate to align with magnetic field, instead of maintaining their original orientation?

[Jarek Duda]

Stern-Gerlach is great idealization of measurement: we start with any (continuous) direction of spin/magnetic dipole, and end with up or down.

If I properly understand, strong magnetic field is sufficient: magnetic dipole precesses in magnetic field, unless being aligned in parallel or anti-parallel way.
Such precession seems related with additional energy, so for energy minimization it aligns up or down ("is measured").

While naively it (also measurnment) looks irreversible, it seems there is also released such energy difference - which would be required to reverse such process.
Like for atom deexcitation, which is reversible if only remembering about released photon carrying energy difference:
"excited atom <-> deexcited atom + photon".

If I properly understand, the gradient of magnetic field is required only for spatial separation of spin up and down beams.

[Bored chemist]

What would happen if the magnetic field used is homogenous?

The particles would all follow the same (curved) path.

What would happen if the magnetic field used is only slightly inhomogenous?

The separation between the "up" and "down" particles would be too small to observe.

If the source is contaminated with particles with zero magnetic moment,

They would pass through in a straight line.

Will it interact with particles with non-zero magnetic moment?

Not really, though there may be simple collisions which would perturb the beams.

why the moving magnets don't rotate to align with magnetic field, instead of maintaining their original orientation?

Given time, they would. A particle which is "the wrong way up" in the magnetic field has an excess of potential energy.
It could shed that energy as a photon, and rotate to line up with the field.

However the excess energy is small so the rate of emission is also small. the particles are in the apparatus for a small fraction of a second. The lifetime of the excited state is much longer than that.

[alancalverd]

BC has summed it up neatly. The basis of a lot of magnetic resonance analysis and imaging is that spin relaxation has a distinct half-life dependent, among other things, on the chemical environment of the target particle. Adding "contamination" to the electron beam would probably reduce the half-life and thus the differentiation from 50/50 to something less spectacular and more difficult to explain.   

[hamdani yusuf (OP)]

The particles would all follow the same (curved) path.

Even if they have opposite spin? Which direction would they go?

[hamdani yusuf (OP)]

Inhomogeneity of magnetic field can be found between like poles of two magnets as shown in picture (c).

Would this produce the same effect as original Stern-Gerlach experiment?

[Bored chemist]

Which direction would they go?

Depends on their charge. Neutral ones would carry on in a straight line (give or take the effect of gravity)

[Bored chemist]

Would this produce the same effect as original Stern-Gerlach experiment?

Possibly, but what you want it the largest possible gradient- a large rate of change of field with distance.