We report a comprehensive study of the ultrafast optoelectronic response of a single self-assembled InGaAs/GaAs quantum dot embedded in a $n\text{\ensuremath{-}}i$-Schottky photodiode device. While manipulation of the artificial atom relies on two independently tunable picosecond pulse trains, sensitive all electrical readout is achieved via photocurrent. We apply our methods to probe the temporal evolution of the quantum dot absorption spectrum following coherent optical generation of a $s$-shell exciton. Our measurements reveal the biexciton absorption as well as previously unobserved $p$-shell transitions that appear in the presence of $s$-shell population. Furthermore, time-resolved measurements allow us to directly monitor the picosecond tunneling times of electrons and holes out of the dot. Beyond these incoherent phenomena, we also demonstrate the potential of our techniques for coherent quantum dot manipulations. Beginning with excitonic Rabi oscillations driven by a single pulse tuned to the neutral exciton we move on to demonstrate the coherent generation of the biexciton via a two-photon nonlinearity, before realizing conditional Rabi oscillations in the exciton-biexciton state manifold. The results provide significant potential for realizing and utilizing conditional coherent dynamics in quantum dot nanostructures for all optical, ultrafast quantum information processing.