Foils are not necessary for all-over lightening but if you choose to use them they can help with sectioning and keeping bleached parts of your hair separate.. Foils can also help keep the bleach from drying out at which point it will no longer lift.
A cap is not necessary but if you decide to use a cap, it should help prevent the bleach from drying out, and prevent it from touching anything you don’t want bleached while you’re waiting for it to process! However, if you are starting from a lighter base color you may not want to use a cap as it can speed up the processing time and you may not need very long!