We report results of large-scale quantum Monte Carlo (QMC) simulations of graphene. Using cutting-edge algorithmic improvements, we are able to consider spatial volumes, corresponding to 20808 electrons, that allow us to access energy scales of direct relevance to experiments. Using constrained random phase approximation (cRPA) estimates of short-ranged interactions combined with a Coulomb tail, we are able to successfully confront numerical and experimental estimates of the Fermi velocity renormalization, thus fixing the parameters of microscopic Hamiltonian to exactly reproduce the experimental data. Subsequent comparison of the QMC results with perturbation theory not only show the non-Fermi liquid character of graphene, but also prove the importance of lattice-scale physics and higher-order perturbative corrections beyond RPA for the quantitative description of the experimental data for the Fermi velocity renormalization in suspended graphene. The same Monte Carlo technique is subsequently employed to investigate electrical transport by computing the renormalization of the optical conductivity in freestanding graphene. The large lattice sizes and low temperatures accessible in our QMC simulations enable a clear resolution of the Dirac plateau in the spectral function, even in the presence of interactions. We demonstrate that, despite the strong renormalization of the single-particle dispersion, the optical conductivity remains essentially constant, in agreement with current experimental observations. This finding points toward the possibility of extending the theorem on the absence of optical conductivity renormalization for the Hubbard model on the hexagonal lattice to the case of long-range interactions.