Can particles enherit constraints from their render object? Example:I have a large sphere that emits particles
and a tiny sphere that the will become each individual particle .

If the original tiny sphere gets a Limit distance to surface constraint,
can each particle also inherit the constraint that the original one has?

So that the particles will stick to the surface of a mesh while moving, even if the mesh is irregular.

I can get similar effect with forces but its very delicate and can fly off the surface easily.
As far as I understand, no. Particles do not inherit constraints. If you want particles to stick to a moving object, make it a collision object and play around with the dampening and stick values.