The Jacobian is singular but Dynare still gives me results

Most of the problem comes from your use of

log(Phi) = (1-rho_phi)*log(STEADY_STATE(Phi)) + rho_phi*log(Phi(-1)) + Eps_phi;

The steady state of Phi cannot be endogenously computed, it seems. If you use

log(Phi) = (1-rho_phi)*log(varphi) + rho_phi*log(Phi(-1)) + Eps_phi;

i.e. replace the steady state operator by the steady state you set in the steady_state_model-block, one of the warnings disappears. For the other shock processes, the problem seems to be the same.