Your son's questions are awesome!
The feet are indeed there, and called Tarsi. Often they have 1 - 3 claws, which can be saw like (serrated) for extra grip.
Many spiders the front (4) legs are directed so stretch forward, and the rear (4) legs streatch backwards, so in total mostly forwards backwards. But, in particular the middle legs can change angle, so help the spider rotate.
Some spiders have primarily sideways legs - laterigrade. Crab spiders in particular. Then indeed movement will often be sideways, but these often prefer just to sit and wait ... so not much movement at all!
Please tell your son i enjoyed his excellent questions!