Help with parallel processing of a viscoelastic stokes flow system

[dokken]

You should use an iterative solver for solving your problem. The default solver used in dolfin is an LU solver, that does not scale well with number of dofs or in parallel.
See for instance:

Not getting a better performance in parallel

There will be different effects for each of the changes you propose. All the step should make parallel computations be more suitable, as increasing the degree for the function space increase the number of dofs (size of the matrix).

and

Fast computation of a large system of PDEs

There are many things you might do. First consider if you want to use a direct or iterative solver: a brief discussion of direct and iterative solvers can for instance be found here and here.