I am familiar with Schlafli symbols for polygons and polygrams, but it gets way more complicated for antiprisms. I get that {7} describes a heptagon, {7/2} describes a heptagram with 7 edges where each edge skips to every 2nd vertex around the shape, and {7/3} describes a heptagram with 7 edges where each edge skips to every 3rd vertex around the shape.
However, looking at an antiprism, 
, the Schlafli symbol is either s{2,2n} or sr{2,n}. Does anyone know how to interpret this?
Finally, does anyone know how to notate with a Schlafli symbol how many vertices are skipped from the top base to the bottom base (or vice versa) in the following crossed antiprisms? Also, does anyone have a good definition for a crossed antiprism? Any help on any part of this is appreciated.
I think your questions should have been split into two posts: one about Schlafli symbols for convex antiprisms, and one about crossed antiprisms. The latter has been answered in comments, so here I'll answer the former. (I hope you're familiar with Schlafli symbols for relatives of the cube $\{4,3\}$, for comparison.)
$\{2\}$ is a digon, a polygon with two edges. $\{n,2\}$ is a dihedron, a polyhedron with two $n$-gon faces. $\{2,n\}$ is a hosohedron, a polyhedron with $n$ digon faces. These can be thought of either as abstract polyhedra, or as polyhedra with curved faces, or as degenerate polyhedra with coincident faces.
(Each polyhedron is shown from a top view and a side view.)
The operations of truncation and rectification can be applied to these:
And then the cantellate $rr\{2,n\}$ can be twisted to make the snub:
As you can see, this is not quite an antiprism; it has some digon faces, and no reflection symmetry.
As a different way to construct the snub, the omnitruncate $tr\{2,n\}$ can be alternated (meaning every other vertex is deleted, so e.g. a decagon becomes a pentagon). But what is alternation exactly, when digons are allowed? Does a square become an edge, or a digon? It is ambiguous.
Well, if the digons are removed in the end, everything seems to work fine.