Can old concrete fragments be cleaned and used as crushed stone?
Recycled concrete is used for several different purposes.  It can be used "as is" for bulk 
fill / drainage / etc.

When cleaned, crushed, and graded for size, it can be used as a base underneath a new concrete pour.

Recycled concrete can also be used as aggregate within the new concrete.  Several factors must be taken into account to ensure that it will not weaken the integrity of the new concrete (moisture retention, etc).  Typically, up to 30% of the aggregate can be replaced with properly processed recycled concrete.

However, concrete is generally recycled in large scale plants where they can reliably clean, crush, sort, and distribute the incoming material.  It is doubtful that you could do this economically in the small scale.

More recycled concrete info