I don't think you need to put a footing for each stringer. Generally ,
it would be ideal on a slab, but I've seen people use those brick and
patio pavers in the dirt as a footing.
As far as anchoring, I used a joist hanger for each stringer at the
top. On the bottom, you should put some kind of anchoring. If you are
using a slab, just anchor each stringer to the slab. Or if you are
putting posts at the bottom for the railing, anchor the stringer to the
posts, and the posts to the ground. But in general, the top anchoring
is most important.