Push from specific directory.

Hi All

I am starting using Git and few queries about it.
1. Is it always necessary to be in root directory to do the push?
2. Can I have a folder structure like
         (a) /Hello-World
         (b) /Hello-World/gitVersion/GitVersionFile.txt and
         (c) /Hello-World/nonGitVersion/NonGitVersionFile.txt
where I give git init for (a) and (c). If Itry to push only from (c) is 
that valid?

Thanks, Anjib