Thank you very much for your answers! Sorry for my wrong statement.

1. I will look into how to identify redundant constraints. I have been reading the Douglass Blanding's book called "Exact Constraint - Machine Design Using Kinematic Processing (1999)" and I find it very enlightening, but I still have practical doubts. Would there be any other reference out there from where to learn how to do this?

2. I have been trying to obtain the Jacobian through a function call but I haven't been able to find a way to do that. I have, though, been able to find a very big Jacobian-related matrix in the solverInformation.txt file, after activating the necessary options in solutionSettings through SimulationSettings():

+++++++++++++++++++++++++++++++
EXUDYN V1.6.0 solver: implicit second order time integration
number of steps = 100000
...
    initial accelerations update Jacobian: Jac    = [[2499.99, ...],[0,2499.99,...],...]
initial accelerations = [...]
  Generalized-alpha: spectralRadius=0.9, alphaM=0.421053, alphaF=0.473684, beta=0.277008, gamma=0.552632, factJacA=0.909091
  has constant mass matrix=0

Is this what I need?

3. To manually obtain the Jacobian myself for the 2D and 3D case of this mechanism, I've been looking up into Chapter 7 of "Modern Robotics - Mechanics, Planning, and Control (2019)" (freely available here), which has the most clear explanations that I have been able to find for closed-chain mechanisms, with specific examples of parallel mechanisms. The book uses Screw Theory though. Do you know any other reference out there?

To obtain the jacobian of your system, you have to use the solver (As static or implicit solvers anyway compute the jacobian). See e.g. the function ComputeLinearizedSystem(..):
https://exudyn.readthedocs.io/en/latest/docs/RST/pythonUtilities/solver.html#function-computelinearizedsystem
and the source code when clicking on the function name. It shows how to compute the jacobian generally. I will add some functionality related to DOF counting soon.