Question 1
What happens if I prescribe a velocity boundary condition to a solid body (a subdomain) which already is has fixed support BC on all its sides? Will the subdomain move or not?

Question 2
What happens if I prescribe velocity BC (for example: V_x =1m/s) and keep the timestep of my dynamic simulation on an order of magnitude smaller (0.1 s)? Will the model prescribe that fractional value of velocity BC to the domain in each of the timestep (for example U_x=0.1m per 0.1s in the above case)?

Regarding question number 1, I would expect no movement overall in case the body is constrained by fixed support on all sides. It’s possible that you will obtain small amount of displacements inside the solid body since the velocity is assigned to whole body while the fixed support is applied to only covering surfaces.

About the second question, yes. In this case, displacement in each time step will be computed by multiplying the time step and velocity unless the body is not constrained by any other boundary conditions.

Indeed that was helpful and I tried implementing the same in my model. However the model subdomain doesn’t seems to moving the way it should. This refers to Run-7 of this model link.
In this model I constrained a rigid body (lower subdomain) using symmetric BC and applied surface parallel velocity, but the displacement seems to still be zero (pic below).