the answer to question 1 is that it depends on what your goal is. If you want to study a model where average inflation is sistematically different from the target, then you should have price adjustment costs/price dispersion in steady state. If instead you are interested in welfare or IRF implications of having different targets, then you should have no dispersion/adjustment costs in steady state. It all depends on the research question you want to answer.
If you go for the second approach, then you should write the Taylor rule and Rotemberg PC as I suggested. And in steady state MC=(epsilon-1)/epsilon. If you go for the first approach, you have two options:
a) You find a closed form solution for the steady state and give it to Dynare, using the command steady_state_model; This is my favourite option.
b) You give to Dynare an initial guess for the steady state, using the command initval.
What you are currently doing is to use the command “steady_state_model” without having a steady-state solution for the Rotemberg case: if you do not have the exact steady state, you cannot use steady_state_model;
The answer to question 2. Normally the Taylor rule is written like this:
where pi_tar coincides with the steady state and R_tar coincides with the steady state nominal rate. The steady-state nominal rate will be always equal to steady-state gross inflation divided by the discount factor. But if you want a model with inflation different from the target in steady state, then also R will be different from the central-bank target: again, you need to find an analytical solution of the steady-state problem.