The on-board flash is mostly useless on any camera. Try sticking some TP over it as a diffuser.
Autofocus speed is dependent on the lens, the kit lens isn't the fastest focus. In general faster apertures help because they let more light onto the AF sensors an diet is easier to measure if a wider aperture lens is out of focus,. However with really wide aperture lens like fast primes the need for accuracy due to the very shallow DoF means that the focus motors turn slower and more controlled.
Autofocus speed is dependent on the lens, the kit lens isn't the fastest focus. In general faster apertures help because they let more light onto the AF sensors an diet is easier to measure if a wider aperture lens is out of focus,. However with really wide aperture lens like fast primes the need for accuracy due to the very shallow DoF means that the focus motors turn slower and more controlled.