  We present a functional renormalization group (fRG) study of the two
dimensional Hubbard model, performed with an algorithmic implementation which
lifts some of the common approximations made in fRG calculations. In
particular, in our fRG flow; (i) we take explicitly into account the momentum
and the frequency dependence of the vertex functions; (ii) we include the
feedback effect of the self-energy; (iii) we implement the recently introduced
multiloop extension which allows us to sum up {\emph{all}} the diagrams of the
parquet approximation with their exact weight. Due to its iterative structure
based on successive one-loop computations, the loop convergence of the fRG
results can be obtained with an affordable numerical effort. In particular,
focusing on the analysis of the physical response functions, we show that the
results become {\emph{independent}} from the chosen cutoff scheme and from the
way the fRG susceptibilities are computed, i.e., either through flowing
couplings to external fields, or through a "post-processing" contraction of the
interaction vertex at the end of the flow. The presented substantial refinement
of fRG-based computation schemes paves a promising route towards future
quantitative fRG analyses of more challenging systems and/or parameter regimes.
