If I modify a submodule, can I push the commit back to the submodule origin, or would that require a clone? If clone, can I store a clone inside another repository?
A submodule is nothing but a clone of a git repo within another repo with some extra meta data (gitlink tree entry, .gitmodules file )
$ cd your_submodule
$ git checkout master
<hack,edit>
$ git commit -a -m "commit in submodule"
$ git push
$ cd ..
$ git add your_submodule
$ git commit -m "Updated submodule"