Our universe contains some (unknown) very large number of particles.

It is also our tenet that our laws of physics should be such as to also apply to a universe with a different number of particles.

That is they should be invariant to the number of particles.

 

So what is motion (ie what are the observables and what do they mean) for a universe containing a single particle?

Is there any field present?

No fields, potential wells or other restrictions are defined other than what the particle 'creates' by virtue of its own existence in an otherwise empty unbounded universe.

Motion is defined with respect to something else. A single particle is at rest with respect to itself, and if that's the only reference you have, then it's at rest. But it's not a realistic scenario.

So what is motion (ie what are the observables and what do they mean) for a universe containing a single particle?

 

Probably the same as in our universe. There is no absolute motion; so with nothing to move relative to there would be no relative motion either.

 

If it's a point particle perhaps you could consider the universe a singularity, with all measures of distance contracted to zero, so all motion occurs across 0 distance.